最大秩映射

关于极大秩的反拟Sasakian流形

On anti-quasi-Sasakian manifolds of maximal rank

本文研究了紧致齐性Riemannian流形与幂零Lie群上极大秩不变反拟Sasakian结构的存在性，证明了前者不存在该结构、后者可完整分类，并指出紧致aqS流形的第二Betti数非零。

Low-dimensional manifolds with non-negative curvature and maximal symmetry rank

We classify closed, simply connected $n$-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions $2\leq n\leq 6$. In dimensions $3k$, $k=1,2$ there is only one such manifold and it is diffeomorphic to the product of $k$ copies of the 3-sphere.

Confocal conics and 4-webs of maximal rank

Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) the net of Apollonian pencils of circles whose foci coincide with the foci of conics, 3) the net of tangents to a conic of the confocal family, we get a planar 4-web. We show that each of these 4-webs is of maximal rank and characterize confocal conics from the web theory viewpoint.

具有最大对称秩的正中间里奇曲率

Positive intermediate Ricci curvature with maximal symmetry rank

该研究推广了Grove和Searle的工作，证明了正中间里奇曲率流形等距群秩的上界，并在最大对称秩情形下获得更强的拓扑刚性结果，涵盖更高曲率及非平凡基本群。

映射类群在极大表示上的作用

The action of the mapping class group on maximal representations

证明了当G = Sp（2n，R），SU（n，n），SO ~*（2n）或Spin（2，n）时，映射类群在闭黎曼曲面的基本群到G的极大表示空间上的适当作用.

三维可积测地流与最大秩网

Integrable geodesic flow in 3D and webs of maximal rank

本文以测地4-网刻画三维空间中具有两个交换二次积分的可积测地流，并证明在自然几何条件下度量为 Stäckel 型。

Non-negatively curved 5-manifolds with almost maximal symmetry rank

We show that a closed, simply-connected, non-negatively curved 5-manifold admitting an effective, isometric $T^2$ action is diffeomorphic to one of $S^5$, $S^3\times S^2$, $S^3\tilde{\times} S^2$ (the non-trivial $S^3$-bundle over $S^2$) or the Wu manifold $SU(3)/SO(3)$.

Non-negatively Curved Manifolds with Maximal Symmetry Rank in Low Dimensions

We classify closed, simply-connected non-negatively curved 5-manifolds admitting an (almost) effective, isometric $T^3$ or $T^2$ action. As a direct consequence, we show that for any manifold, of dimensions up to and including 9 under the same hypotheses, the maximal symmetry rank is equal to $[2n/3]$ and the free rank is less than or equal to one half that value.

Canonical frames for distributions of odd rank and corank 2 with maximal first Kronecker index

We construct canonical frames and find all maximally symmetric models for a natural generic class of corank 2 distributions on manifolds of odd dimension greater or equal to 7. This class of distributions is characterized by the following two conditions: the pencil of 2-forms associated with the corresponding Pfaffian system has the maximal possible first Kronecker index and the Lie square of the subdistribution generated by the kernels of all these 2-forms is equal to the original distribution. In particular, we show that the unique, up to a local equivalence, maximally symmetric model in thi…

具有几乎最大对称秩的正曲流形的同胚分类

Homeomorphism Classification of positively curved manifolds with almost maximal symmetry rank

本文证明了一个3-环面（4-环面）等距作用于其上的正截面曲率闭单连通8-流形（9-流形）同胚于球面、复射影空间或四元数射影平面（球面）.本文证明了一个具有正截面曲率的单连通2 m-闭流形（m>4）与一个复射影空间同胚当且仅当它的欧拉示性数不为2.根据Wilking的一个结果，这些结果暗示了几乎最大对称秩的正曲n-流形（n>7）的同胚分类[ \frac{n-1} 2].

小RCD(K,N)空间的最大秩的拓扑刚性

Topological rigidity of small RCD(K,N) spaces with maximal rank

研究显示，小RCD(K,N)空间在最大秩条件下具有拓扑刚性，与infranilmanifold同胚，扩展了Kapovitch-Wilking的结果至非光滑环境。

The geometry of maximal components of the PSp(4,R) character variety

In this paper we describe the space of maximal components of the character variety of surface group representations into PSp(4,R) and Sp(4,R). For every rank 2 real Lie group of Hermitian type, we construct a mapping class group invariant complex structure on the maximal components. For the groups PSp(4,R) and Sp(4,R), we give a mapping class group invariant parameterization of each maximal component as an explicit holomorphic fiber bundle over Teichmüller space. Special attention is put on the connected components which are singular, we give a precise local description of the singularities an…

具有最大离散对称秩的正曲流形

Positively curved manifolds with maximal discrete symmetry rank

设M是一个单连通的正截面曲率n维闭流形。如果M也允许一个大秩的等距初等p-群作用，则我们确定它的同胚或同伦型.我们的主要结果是：存在常数p（n）>0使得（1）若M^{2n}对素数p \ge p（n）有有效等距\Bbb Z_p^k作用，则k \le n和"=“意味着M^{2n}同胚于球面或复射影空间. (2)若M^{2n+1}对于素数p \ge p（n）允许等距S^1 x \Bbb Z_p^k-作用，则k \le n和"=“意味着M同胚于球面. (3)对（1）或（2）中的M，若n \ge 7，k \ge [ \frac{3n} 4]+2，则M同胚于球面或同伦于复射影空间.

极大增长分布的存在性与分类

Existence and classification of maximal growth distributions

该文研究光滑流形上极大增长分布的存在性与分类，证明秩>2的极大增长分布满足完全h原理，建立微分关系丰度检验新准则，正面解答了相关长期公开问题，同时说明秩2情形的非丰度性。