弱Landsberg流形的一个整体刚性定理

研究弱Landsberg流形的整体刚性性质,并证明任一闭的具负旗曲率的弱Landsberg 流形一定是Riemann流形.     

具有相对迷向Landsberg曲率的球对称Finsler度量（英文）

得到了可以刻画具有相对迷向Landsberg曲率的球对称Finsler度量的方程.作为它的应用,构造了新的具有相对迷向Landsberg曲率的Finsler度量.     

具有迷向S曲率Randers度量的几何意义

Riemann流形上的Zermelo航行为Randers度量提供了一个简洁而且清晰的几何背景．在这个背景下D．Bao，C．Robles和Z．Shen对于具有常旗曲率的Randers度量进行了完全分类．这篇论文中，我得到了判定具有特殊曲率性质的Randers度量的两个充分必要条件．从这两个条件出发，我得到了迷向S曲率的Randers度量的几何意义和一系列推论，并且构造了具有迷向S曲率Randers度量的新例子．最后，在Zermelo航行的背景下研究了Berwald型的Raiders度量．     

拟常曲率流形中有平行平均曲率向量的子流形

研究了拟常曲率流形中具有平行平均曲率向量的子流形,给出了两个积分不等式.     

余辛流形的半不变子流形的Ricci曲率

本文研究了余辛流形的半不变子流形,得到了这类子流形的Ricci曲率与平均曲率平方之间的—个不等式,并讨论了等式成立的充分必要条件．     

拟常曲率Riemann流形中的伪脐点子流形

研究了拟常曲率Riemann流形中具有平行平均曲率向量的伪脐点子流形,得到了一个Simons型公式．     

具有平行平均曲率向量场的子流形

本文讨论了具有平行平均曲率向量场的某一类子流形，得到了这类子流形成为全脐点子流形及其余维数减小的充分条件。     

LP—Sasaki流形的某些无穷小变换

M.Okumura曾证明了Sasaki流形中保持曲率的无穷小变换必定是无穷小等距变换。K.Matsumoto 在[2]中对于 P-Sasaki 流形讨论了同样的无穷小变换。得到的主要结果为定理 A 在满足φ~2(n-1)~2≠0的 P-Sasaki 流形中,每个保持曲率的无穷小变换必定是无穷小自同构变换。本文将在更为广泛的 LP-Sasaki 流形中讨论这同一问题,主要证明如下定理:     

伪黎曼空间型的2一调和类空子流形

用活动标架法给出常曲率的伪黎曼流形的类空子流形为2-调和的充要条件,研究平均曲率为零的一些条件.     

具有平行平均曲率向量子流形的曲率估计与稳定性

本文估计空间形式中具有平行平均曲率向量子流形上共形度量的数量曲率上界,并利用其研究了具有常平均曲率超曲面的稳定性．     

Properties of Berwald scalar curvature

We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. For (α,β)-metrics on manifold of dimension greater than 2, if the mean Landsberg curvature and the Berwald scalar curvature both vanish, then the Berwald curvature also vanishes.     

A global rigidity theorem for weakly Landsberg manifolds

In this paper we study a global rigidity property for weakly Landsberg manifolds and prove that a closed weakly Landsberg manifold with the negative flag curvature must be Riemannian.     

On projective symmetries on Finsler spaces

There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves of I-invariant projective vector fields. The sub-algebra of the C-projective vector fields, leaving the H-curvature invariant, has been studied extensively. Here we show on a closed Finsler space with negative definite Ricci curvature reduces to that of Killing vector fields. Moreover, if an Einstein-Finsler space admits such a projective vector field then the flag curvature is constant. Finally, a classification of compact isotropic mean Landsberg manifolds admitting certain projective vector fields is obtained with respect to the sign of Ricci curvature.     

On the class of generalized Landsberg manifolds

In 2000, Bejancu–Farran introduced the class of generalized Landsberg manifolds which contains the class of Landsberg manifolds. In this paper, we prove three global results for generalized Landsberg manifolds. First, we show that every compact generalized Landsberg manifold is a Landsberg manifold. Then we prove that every complete generalized Landsberg manifold with relatively isotropic Landsberg curvature reduces to a Landsberg manifold. Finally, we show that every generalized Landsberg manifold with vanishing Douglas curvature satisfies \(\mathbf{H}=0\).     

S-curvature of Doubly Warped Product of Finsler Manifolds

Doubly warped product of Finsler manifolds is useful in theoretical physics, particularly in general relativity. In this paper, we study doubly warped product of Finsler manifolds with isotropic mean Berwald curvature or weak isotropic S-curvature.     

The rigidity theorem for harmonic maps from Berwald manifolds

In this paper, we can prove that any non‐degenerate strongly harmonic map ? from a compact Berwald manifold with nonnegative general Ricci curvature to a Landsberg manifold with non‐positive flag curvature must be totally geodesic, which generalizes the result of Eells and Sampson ([2]).     

Finsler Manifolds with Positive Constant Flag Curvature

It is shown that a Finsler metric with positive constant flag curvature and vanishing mean tangent curvature must be Riemannian. As applications, we also discuss the case of Cheng's maximal diameter theorem and Green's maximal conjugate radius theorem in Finsler manifolds.     

The main invariants of a complex finsler space

In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwald frame. The geometry of such manifolds is controlled by three real invariants which live on T'M: two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular interest. Complex Berwald spaces coincide with Kähler spaces, in the two – dimensional case. We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the Kähler purely Hermitian spaces by the fact K = W = constant and I = 0. For the class of complex Berwald spaces we have K = W = 0. Finally, a classification of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained.     

Some curvature properties of Cartan spaces with mth root metrics

In this paper, we define some non-Riemannian curvature properties for Cartan spaces. We consider a Cartan space with the mth root metric. We prove that every mth root Cartan space of isotropic Landsberg curvature, or isotropic mean Landsberg curvature, or isotropic mean Berwald curvature reduces to a Landsberg, weakly Landsberg, and weakly Berwald spaces, respectively. Then we show that the mth root Cartan space of almost vanishing H-curvature satisfies H?=?0.     

Riemannian Manifold in Which the Skew-Symmetric Curvature Operator has Pointwise Constant Eigenvalues

We study manifolds where the natural skew-symmetric curvature operator has pointwise constant eigenvalues. We give a local classification (up to isometry) of such manifolds in dimension 4. In dimension 3, we describe such manifolds up to a classification of three - dimensional Riemannian manifolds with principal Ricci curvatures r₁ = r₂ = 0, r₃- arbitrary. We give examples of such manifolds in all dimensions which do not have constant sectional curvature; these manifolds are not pointwise Osserman manifolds in general.