Paul-Andi Nagy
We study Riemannian foliations with complex leaves on Kaehler manifolds. The tensor T, the obstruction to the foliation be totally geodesic, is interpreted as a holomorphic section of a certain vector bundle. This enables us to give classification results when the manifold is compact.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We consider strict and complete nearly Kaehler manifolds with the canonical Hermitian connection. The holonomy representation of the canonical Hermitian connection is studied. We show that a strict and complete nearly Kaehler is locally a Riemannian product of homogenous nearly Kaehler spaces, twistor spaces over quaternionic Kaehler manifolds and 6-dimensional nearly Kaehler manifolds. As an application we obtain structure results for totally geodesic Riemannian foliations admitting a compatible Kaehler structure. Finally, we obtain a classification result for the homogenous case, reducing a …
The purpose of this paper is to study the canonical foliations of a quaternion CR-submanifold of an almost quaternion Kaehler product manifold.
The purpose of this paper is to establish a partial regularity theory on certain homogeneous complex Monge-Ampere equations. As consequences of this new theory, we prove the uniqueness of extremal Kaehler metrics and give an necessary condition for existence of extremal Kaehler metrics.
We study the moduli space of quaternionic Kaehler structures on a compact manifold of dimension 4n (n>2) from a point of view of Riemannian geometry, not twistor theory. Then we obtain a rigidity theorem for quaternionic Kaehler structures of nonzero scalar curvature by observing the moduli space.
We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.
We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems for compact foliations in Kaehler manifolds of Edwards-Millett-Sullivan and Hollman.
We describe a family of locally conformal Kaehler metrics on class 1 Hopf surfaces H containing some recent metrics constructed by P. Gauduchon and L. ornea. We study some canonical foliations associated to these metrics, in particular a 2-dimensional foliation E that is shown to be independent of the metric. We elementary prove that E has compact leaves if and only if H is elliptic. In this case the leaves of E give explicitly the elliptic fibration of H, and the natural orbifold structure on the leaf space is illustrated.
B. Sahin [9] introduced the notion of anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In the present paper we extend the notion of anti-invariant and Lagrangian Riemannian submersions (a special anti-invariant Riemannian submersion) to the case of locally conformal Kaehler manifolds. We discuss the geometry of foliation and obtain some decomposition theorems for the total manifold of such submersions.
Rigidity of Nilpotent Lie Foliations: Cohomological Obstructions and Classification
本文发展了研究nilpotent Lie foliations在solvable变形下的刚性的系统上同调框架，证明了变形障碍在于cohomology群H²(𝑔,𝑔/[𝑔,𝑔])，并建立了基于广义海森堡群H_{2k+1}的刚性判据。
We study generic Riemannian submersions from nearly Kaehler manifolds onto Riemannian manifolds. We investigate conditions for the integrability of various distributions arising for generic Riemannian submersions and also obtain conditions for leaves to be totally geodesic foliations. We obtain conditions for a generic Riemannian submersion to be a totally geodesic map and also study generic Riemannian submersions with totally umbilical fibers. Finally, we derive conditions for generic Riemannian submersions to be harmonic map.
We show that if the structure algebra of a Riemannian foliation F on a closed manifold M is nilpotent, then the integral of the Álvarez class of (M,F) along every closed path is the exponential of an algebraic number. By this result and the continuity of the Álvarez class under deformations shown in arXiv:1009.1098v2, we prove that the Álvarez class and the geometrically tautness of Riemannian foliations on a closed manifold M are invariant under deformation, if the fundamental group of M has polynomial growth.
Morse-Novikov cohomology and rigidity of Lie affine foliations
研究二维非阿贝尔李代数仿射(1)建模的李叶状结构的刚性，通过Morse-Novikov上同调给出消失条件，证明3或4维紧致可定向流形上的李仿射叶状结构在形变下是刚性的。
The higher fixed point theorem for foliations. Applications to rigidity and integrality
本文应用叶状结构的高阶Lefschetz定理与Haefliger上同调，构造数值不变量以阻碍保持叶片的紧致群作用，并建立相关整性结果。
Rigidity of Lie foliations with locally symmetric leaves
本文证明极小李叶状结构的叶若局部等距于无庞加莱圆盘因子的非紧型对称空间，则光滑共轭于齐次李叶状结构，推广了Zimmer定理，并应用于和乐群算术性与黎曼叶状结构刚性。
Rigidity of singular de-Sitter tori with respect to their lightlike bi-foliation
本文研究了具有锥形奇点的洛伦兹面的刚性，证明了德西特环面由其光状双分层的拓扑等价类确定。
The purpose of the article is to study a foliation associated to a lattice-equivariant harmonic map of small rank from a complex ball to another. The result is related to rigidity of some complex ball quotients.
We study perturbations of a partially hyperbolic toral automorphism L which is diagonalizable over C and has a dense center foliation. For a small perturbation of L with a smooth center foliation we establish existence of a smooth leaf conjugacy to L. We also show that if a small perturbation of an ergodic irreducible L has smooth center foliation and is bi-Holder conjugate to L, then the conjugacy is smooth. As a corollary, we show that for any symplectic perturbation of such an L any bi-Holder conjugacy must be smooth. For a totally irreducible L with two-dimensional center, we establish a n…
Any Kaehler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dimension.
In this paper, we study the existence of various harmonic maps from Hermitian manifolds to Kaehler, Hermitian and Riemannian manifolds respectively. By using refined Bochner formulas on Hermitian (possibly non-Kaehler) manifolds, we derive new rigidity results on Hermitian harmonic maps from compact Hermitian manifolds to Riemannian manifolds, and we also obtain the complex analyticity of pluri-harmonic maps from compact complex manifolds to compact Kaehler manifolds (and Riemannian manifolds) with non-degenerate curvatures, which are analogous to several fundamental results in [28,Siu], [14,J…
3-quasi-Sasakian manifolds were studied systematically by the authors in a recent paper as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. This paper throws new light on their geometric structure which reveals to be generally richer compared to the 3-Sasakian subclass. In fact, it turns out that they are multiply foliated by four distinct fundamental foliations. The study of the transversal geometries with respect to these foliations allows us to link the 3-quasi-Sasakian manifolds to the more famous hyper-Kaehler and quaternionic-Kaehler geometries. Furthermore, we stron…
We study the totally null surfaces of the neutral Kaehler metric on certain 4-manifolds. The tangent spaces of totally null surfaces are either self-dual ($α$-planes) or anti-self-dual ($β$-planes) and so we consider $α$-surfaces and $β$-surfaces. The metric of the examples we study, which include the spaces of oriented geodesics of 3-manifolds of constant curvature, are anti-self-dual, and so it is well-known that the $α$-planes are integrable and $α$-surfaces exist. These are holomorphic Lagrangian surfaces, which for the geodesic spaces correspond to totally umbilic foliations of the underl…
We derive general structure and rigidity theorems for submetries $f: M \to X$, where $M$ is a Riemannian manifold with sectional curvature $\sec M \ge 1$. When applied to a non-trivial Riemannian submersion, it follows that $diam X \leq π/2 $. In case of equality, there is a Riemannian submersion $\mathbb{S} \to M$ from a unit sphere, and as a consequence, $f$ is known up to metric congruence. A similar rigidity theorem also holds in the general context of Riemannian foliations.
Infinitesimally rigid Lie foliations with dense leaves
本文研究了具有稠密叶的李叶的微小刚性，构造了基于任意紧致单李代数（非so(3))的微小刚性李叶形变。
A rigidity result for coisotropic submanifolds in contact geometry
本文研究接触流形中紧致正则余迷向子流形的余迷向形变，证明了在特征叶层微分同胚的邻近子流形中其具有刚性，并结合经典叶层刚性结果推广至所有邻近子流形。
Let $(M,\mathcal{F})$ be a closed manifold with a Riemannian foliation. The Álvarez class is the cohomology class of degree 1 of $M$ whose triviality characterizes the minimizability of $(M,\mathcal{F})$. We show that the integral of the Álvarez class along every closed path in $M$ is the logarism of an algebraic integer if $π_{1}M$ is polycyclic or $\mathcal{F}$ is of polynomial growth.
Generalized Semi-Riemannian Submersions and Foliations
本文引入广义半黎曼浸没与叶状结构概念，建立正则叶状结构为广义半黎曼的充要条件，证明平稳横截叶状结构的诱导性质，得到时空上平稳类光叶状结构的刚性结果，并推导奥尼尔型截面曲率公式。
A rigidity theorem for Einstein $4$-manifolds with sectional curvature of a fixed sign, and its consequences
研究具有半定截面曲率的4维爱因斯坦度量，通过刻画满足特定逐点不等式的此类度量，得出一系列推论，包括在非正曲率闭爱因斯坦及凯勒 - 爱因斯坦4维流形研究中的应用，还得到了凯勒 - 爱因斯坦情形下的尖锐不等式。
First we confirm a conjecture asserting that any compact Kähler manifold $N$ with $\Ric^\perp>0$ must be simply-connected by applying a new viscosity consideration to Whitney's comass of $(p, 0)$-forms. Secondly we prove the projectivity and the rational connectedness of a Kähler manifold of complex dimension $n$ under the condition $\Ric_k>0$ (for some $k\in \{1, \cdots, n\}$, with $\Ric_n$ being the Ricci curvature), generalizing a well-known result of Campana, and independently of Kollár-Miyaoka-Mori, for the Fano manifolds. The proof utilizes both the above comass consideration and a secon…
A curvature approach to fatness
本文通过曲率方法研究胖黎曼淹没，分类纤维为对称空间，建立胖叶理与陪集叶理的等距对应，并证明对偶叶理的刚性。
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We motivate the definition of weak equivalence (found in the literature) by studying different interpretations of the concept `singular Lagrangian foliation'. Finally, we prove a normal form theorem inspired by the Moser path method. In the second part we study the deformation theory of a PDE with a pseudogroup of symmetries in general. We prove that a solution is ri…
Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such foliations by studying the infinitesimal model associated to the canonical connection. We also establish results for symmetric spaces of non-compact type and a general rigidity result for any irreducible Kähler manifold.
On the Lie Foliation structure of Walker Manifolds
本文研究Walker流形的结构，证明其null平行分布可积分为G-Lie流形，并探讨Ricci曲率与流形维度的关系，提出局部分类和刚性定理。
Schwarz lemmas and rigidity of \(\bar\partial_b\)-harmonic maps
本文证明从完备伪厄米流形到负曲率Kähler流形的\\(\bar\partial_b\\)-调和映射的Schwarz引理，并利用Bochner恒等式和Siu型散度恒等式，在Sasakian源和复双曲目标上分类达到水平界的映射，导出叶状结构、多重调和性和秩刚性。
$C^0$-Poisson geometry, coisotropic submanifolds, and clean intersection points
本文研究了Poisson同胚的刚性与非刚性，证明了共切子流形的$C^0$刚性，并引入了$C^0$-特征划分作为拓扑不变量。
A harmonic map from a Riemannian manifold into a Grassmannian manifold is characterized by a vector bundle, a space of sections of this bundle and a Laplace operator. We apply our main theorem, itself a generalization of a Theorem of Takahashi, to generalize the theory of do Carmo and Wallach and to describe the moduli space of harmonic maps satisfying the gauge and the Einstein-Hermitian conditions from a compact Rieannian manifold into a Grassmannian. As an application, several rigidity results are exihibited. In particular we generalize a rigidity theorem due to Calabi in the case of holomo…
This is Part II of a series on noncompact isometry groups of Lorentz manifolds. We have introduced in Part I, a compactification of these isometry groups, and called ``bi-polarized'' those Lorentz manifolds having a ``trivial '' compactification. Here we show a geometric rigidity of non-bi-polarized Lorentz manifolds; that is, they are (at least locally) warped products of constant curvature Lorentz manifolds by Riemannian manifolds.
We continue the program of Chinea, De Leon and Marrero who studied the topology of cosymplectic manifolds. We study 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kaehler structures. We show that there is an action of the Lie algebra so(4,1) on the basic cohomology spaces of a compact 3-cosymplectic manifold with respect to the Reeb foliation. This implies some topological obstructions to the existence of such structures which are expressed by bounds on the Betti numbers. It is known that every 3-cosymplectic manifold is a local Riemannian product of a hyper-K…
Scalar curvature comparison and rigidity of $3$-dimensional weakly convex domains
本文证明了具有平均凸边界的紧致黎曼3-流形在标量曲率非负且满足缩放平均曲率比较时是平坦的，并将结果推广至带角流形，其证明利用了毛细极小曲面和叶状结构。
We consider an optical hypersurface $Σ$ in the cotangent bundle $τ:T^*M\to M$ of a closed manifold $M$ endowed with a twisted symplectic structure. We show that if the characteristic foliation of $Σ$ is Anosov, then a smooth 1-form $θ$ on $M$ is exact if and only $τ^*θ$ has zero integral over every closed characteristic of $Σ$. This result is derived from a related theorem about magnetic flows which generalizes our work in \cite{DP}. Other rigidity issues are also discussed.
Clairaut semi-invariant Riemannian maps to Kaehler manifolds
本文回顾克莱罗黎曼映射（CRM）概念并给出相关性质，定义克莱罗半不变黎曼映射（CSIRM）及非平凡例子，推导其成为调和、全测地映射等的充要条件及分布相关性质。
Foliated Plateau problems, surface Radon transforms, and boundary area rigidity in dimension three
本文研究三维黎曼球上由椭圆曲率泛函定义的 $\Phi$-曲面，通过求解叶状 Plateau 问题构造单位切丛的叶状结构，分析曲面 Radon 变换的核与单射性，并应用于极小曲面叶状结构下的边界面积刚性问题的解决。
A Lower Bound for the First Non-zero Basic Eigenvalue on a Singular Riemannian Foliation
本文研究了奇异黎曼流形上第一个非零基本特征值的下界，并给出了相应的刚性结果。
For a Riemannian submersion from a simple compact Lie group with a bi-invariant metric, we prove the action of its holonomy group on the fibers is transitive. As a step towards classifying Riemannian submersions with totally geodesic fibers, we consider the parameterized surface induced by lifting a base geodesic to points along a geodesic in a fiber. Such a surface is "doubly ruled" (it is ruled by horizontal geodesics and also by vertical geodesics). Its characterizing properties allow us to define "doubly ruled parameterized surfaces" in any Riemannian manifold, independent of Riemannian su…
The basic Dolbeault cohomology groups of a Sasakian manifold M are invariants of its characteristic foliation F (the orbit foliation of the Reeb flow). We show some fundamental properties of this cohomology, which are useful for its computation. In the first part of the article, we show that the basic Hodge numbers, the dimensions of the basic Dolbeault cohomology groups, only depend on the isomorphism class of the underlying CR structure. Equivalently, we show that the basic Hodge numbers are invariant under deformations of type I. This result reduces their computation to the quasi-regular ca…
A foliated manifold (M,F) is minimizable if there exists a Riemannian metric g on M such that every leaf of F is a minimal submanifold of (M,g). Alvarez Lopez defined a cohomology class of degree 1 called the Alvarez class of (M,F) whose triviality characterizes the minimizability of (M,F), when M is closed and F is Riemannian. In this paper, we show that the family of the Alvarez classes of a smooth family of Riemannian foliations is continuous with respect to the parameter. Since the Alvarez class has algebraic rigidity under certain topological conditions on (M,F) as the author showed in ar…
Symmetries of geodesic flows on covers and rigidity
本文定义并研究了非紧流形上 Anosov 系统提升的叶状中心化子，证明了具有夹紧负截面曲率的闭 Riemannian 流形测地流在万有覆盖上的叶状中心化子具有有限维 Lie 群等刚性性质。
In this paper we study the variability and rigidity of secondary characteristic classes which arise from flat connections on a manifold. Considering the connection as a Lie-algebra valued one-form, we study the characteristic map from Lie algebra cohomology to de Rham cohomology of the manifold, and prove that if the Leibniz cohomology of the Lie algebra vanishes, then all secondary characteristic classes are rigid. In the case of codimension one foliations (with trivial normal bundle), we show that a characteristic map from the Leibniz cohomology of formal vector fields to the de Rham cohomol…
Let G be a simple Lie group of real rank one, and S the ideal boundary of the corresponding symmetric space of noncompact type (H^n_R, H^n_C, H^n_H or H^2_O). We show the finiteness of the possible values of the secondary characteristic classes of transversely homogeneous foliations on a fixed manifold whose transverse structures are modeled on the G-action on S, except the case where G=SO(n+1,1) for even n. For this exceptional case, we construct examples of foliations on a manifold which break the finiteness and show a weaker form of the finiteness. These are generalizations of a finiteness …
Ricci Curvature and Betti Numbers of Hessian Manifolds
研究Hessian度量在由第一Koszul形式生成的codimension-one foliation叶上的Ricci曲率性质，发现单叶非负Ricci曲率迫使Hessian度量为平坦，且给出Betti数的精确界。
We describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM- and LVMB-manifolds and, in most generality, complex manifolds with a maximal holomorphic torus action. We also provide a dga model for the ordinary Dolbeault cohomology algebra. The Hodge decomposition for the basic Dolbeault cohomology is proved by reducing to the transversely Kaehler (equivalently, polytopal) case using a foliated analogue of toric blow-up.
On global rigidity of transversely holomorphic Anosov flows
本文研究了横向全纯Anosov流的全局刚性，证明了其在特定条件下可积分到复流形，并给出了拓扑transitive流的轨道等价结果。
Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint. We describe a complex analogue of the classical Godbillon-Vey invariant, the so-called Bott invariant, and a logarithmic monodromy of closed leaves. The Bott invariant allows us to formulate a generalised Gauß-Bonnet theorem. We compute these invariants for the Poincaré foliations on the 3-sphere and derive rigidity statements, including a uniformisation theo…
We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on manifolds with boundary of dimension n>=3. We also present an inversion formula. Under the condition that the manifold can be foliated with a continuous family of strictly convex surfaces, we prove a global result which also implies a lens rigidity result near such a metric. The class of manifolds satisfying the foliation condition includes manifolds with no focal points, and does not exclude existence of conjugate p…
Let $(\mathcal{M},g)$ be a compact Riemannian manifold of dimension $N$, $N\geq 2$. In this paper, we prove that there exists a family of domains $(Ω_\varepsilon)_{\varepsilon\in(0,\varepsilon_0)}$ and functions $u_\varepsilon$ such that $ -Δ_{g} u_\varepsilon=1 \quad \textrm{ in } Ω_\varepsilon, \quad u_\varepsilon=0 \quad\textrm{ on }\partialΩ_\varepsilon, \quad {g}(\nabla_{ {g}} {u_\varepsilon}, ν_\varepsilon)=-\frac{\varepsilon}{N} \quad \textrm{ on }\partialΩ_\varepsilon, $ where $ν_\varepsilon$ is the unit outer normal of $\partialΩ_\varepsilon$. The domains $Ω_\varepsilon$ are smooth pe…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。