奇异德西特环面相对于其光状双分层的刚性

类空叶理的不存在性与洛伦兹几何中的优势能量条件

Nonexistence of spacelike foliations and the dominant energy condition in Lorentzian geometry

我们证明了许多维数>2的洛伦兹流形不允许类空余维1叶理，并且几乎所有维数>2的流形都允许洛伦兹度量满足支配能量条件和类时收敛条件。这两个看似无关的说法其实有着相同的起源。我们还讨论了广义相对论中的拓扑变化问题。提普勒的一个定理说，拓扑变化是不可能通过时空协边，其里奇曲率满足严格的类光收敛条件。在他的定理中，要求配边的边界是类空的。我们表明，拓扑结构的变化与严格的类光收敛条件，也占主导地位的能量条件是可能的，在许多情况下，而不是只需要存在一个类时向量场是横向的边界。

紧复环面上的湍流全纯叶状结构与横截全纯Cartan几何

Turbulent holomorphic foliations on compact complex tori and transversely holomorphic Cartan geometry

本研究定义了紧复环面上推广Ghys余维一情形的高余维非奇异全纯湍流叶状结构，证明其所有横截全纯Cartan几何均平坦，并给出了该几何的唯一性结果。

Masur's Divergence for Tori and Kummer Surfaces

Masur's divergence states that the horizontal foliation of translation surfaces is uniquely ergodic if the geodesic flow is recurrent on the moduli space. This established a relationship between geometrical properties of foliations and the dynamics on the moduli space. In this paper, we extend this theorem to complex torus and Kummer surfaces. We define and calculate horizontal foliations and the corresponding geodesic flow in the moduli space of Kähler metrics and prove that the horizontal foliation is uniquely ergodic if the geodesic flow is recurrent. We also find the a necessary algebraic …

Riemannian foliation with exotic tori as leaves

We construct smooth fiber bundles such that the fibers are exotic tori and the total space has finite abelian fundamental group. This gives examples of a Riemannian foliation on a closed manifold whose leaves are exotic tori and whose total space has finite abelian fundamental group.

洛伦兹度规空间的动力学性质

Dynamical properties of the space of Lorentzian metrics

本文研究了紧致流形上的洛伦兹度量空间上的超同态群作用的非适当性的机制。特别是，我们证明了nonpropriness需要存在的lightlike测地线叶理的余维1。在2-环面上，我们证明了沿其类光叶理之一具有常曲率的度量实际上是平坦的。这使我们能够表明，限制的行动，以非平坦的度量是适当的，并在一组平坦的度量卷1的行动是遍历的。最后，我们表明，相反的黎曼的情况下，度量空间没有等距并不总是开放的。

Riemannian Foliations and the Topology of Lorentzian Manifolds

A parallel lightlike vector field on a Lorentzian manifold $X$ naturally defines a foliation $\mathcal{F}$ of codimension one. If either all leaves of $\mathcal{F}$ are compact or $X$ itself is compact admitting a compact leaf and the (transverse) Ricci curvature is non-negative then a Bochner type argument implies that the first Betti number of $X$ is bounded by $1 \leq b_{1} \leq \dim X$ if $X$ is compact and $0 \leq b_{1} \leq \dim X -1$ otherwise. We show that these bounds are optimal and depending on the holonomy of $X$ we obtain further results. Finally, we classify the holonomy represen…

Monge surfaces and planar geodesic foliations

A Monge surface is a surface obtained by sweeping a generating plane curve along a trajectory that is orthogonal to the moving plane containing the curve. Locally, they are characterized as being foliated by a family of planar geodesic lines of curvature. We call surfaces with the latter property PGF surfaces, and investigate the global properties of these two naturally defined objects. The only compact orientable PGF surfaces are tori; these are globally Monge surfaces, and they have a simple characterization in terms of the directrix. We show how to produce many examples of Monge tori and Kl…

Riemannian foliations and geometric quantization

We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to symplectic toric quasi-folds, suspensions of isometric actions of discrete groups, and K-contact manifolds are discussed.

最简单 Morse-Bott 叶状结构在透镜空间上的微分同胚群的同伦类型，2

Homotopy types of diffeomorphisms groups of simplest Morse-Bott foliations on lens spaces, 2

本文证明透镜空间上最简单 Morse-Bott 叶状结构的保叶微分同胚群到不交换奇异圆的叶状微分同胚群的包含映射是同伦等价。

二维余维数的紧致单连通微分流形上的A-叶结构

A-Foliations of codimension two on compact simply-connected manifolds

该研究证明二维余维数的紧致单连通微分流形上的奇异Riemann叶结构可通过光滑有效$n$- торus作用给出，解决了关于exotic торi叶结构存在的问题。

The topology of Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)

In this paper we study topological properties of an integrable case for Euler's equations on the Lie algebra $\textrm{so}(4)$, which can be regarded as an analogue of the classical Kovalevskaya case in rigid body dynamics. In particular, for all values of the parameters of the system under consideration the bifurcation diagrams of the momentum mapping are constructed, the types of critical points of rank $0$ are determined, the bifurcations of Liouville tori are described and the loop molecules for all singular points of the bifurcation diagram are computed. It follows from the obtained result…

Riemann Surface上的一般Hamilton叶状结构的拓扑

Topology of the Generic Hamiltonian Foliations on the Riemann Surface

研究了由一般全纯1-形式的实部给出的黎曼曲面上一般Hamilton动力系统的拓扑。我们的方法是基于循环的transmittance规范基（TCB）的概念。这种方法使我们能够提出一个方便的组合模型的整个拓扑结构的流，特别是有效的g=2。这里需要黎曼曲面上的极大阿贝尔覆盖。建立了该流程的完整组合模型。它由平面图和g直线流在“有障碍物”的二维圆环中的流动组成。研究了横截叶理的正闭路的基本半群及其轨迹的拓扑特征。这项工作包含了作者最近的预印本（arXiv数学。GT/0105338）和新的结果计算所有的TCB在2-环面障碍，在连分数方面的改进的阐述。

横截仿射叶状结构的堆叠几何与对数拓扑

Stacky geometry and logarithmic topology of transversely affine foliations

研究横截仿射叶状结构关联的堆叠与对数拓扑结构，通过holonomy群与商堆叠给出乘性发展坐标的几何基础，并利用Kato-Nakayama空间刻画边界线性动力学与对数提升。

可积系统中$A_n$奇点普适开折的辛分类

Symplectic classification for universal unfoldings of $A_n$ singularities in integrable systems

本文研究可积哈密顿系统中$A_n$奇点普适开折的辛分类问题，得到局部、半局部辛正规形及半全局拉格朗日叶状结构分类，明确了不同情形下的辛不变量与结构稳定性。