双扭曲积Hermitian流形

主要研究双扭曲积Hermitian流形的各种曲率,给出了紧致非平凡的双扭曲积Hermitian流形具有常全纯截面曲率的充要条件,得到了一种构造满足第一或第二爱因斯坦条件的Hermitian流形的有效方法.     

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.     

S-curvature of isotropic Berwald metrics

Isotropic Berwald metrics are as a generalization of Berwald metrics. Shen proved that every Berwald metric is of vanishing S-curvature. In this paper, we generalize this fact and prove that every isotropic Berwald metric is of isotropic S-curvature. Let F = α + β be a Randers metric of isotropic Berwald curvature. Then it corresponds to a conformal vector field through navigation representation.     

Non-existence of Warped Product Semi-Slant Submanifolds of Kaehler Manifolds

In this paper, we show that there are no warped product semi-slant submanifolds of Kaehler manifolds. Contrary to this result,we provide an elementary example of a CR-warped product submanifold of a Kaehler manifold     

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．     

Warped products with special Riemannian curvature

We study the geometry of particular classes of Riemannian manifolds obtained as warped products. We focus on the case of constant curvature which is completely classified and on the Einstein case. This study provides nontrivial instances of Einstein manifolds which are warped product of Einstein factors.Supported by a grant from Università di Parma     

Rigidity of Noncompact Finsler Manifolds

For a Euclidean space or a Minkowski space, we change the metric in a compact subset and show that the resulting Finsler manifold is isometric to the original standard space under certain conditions. We assume that the mean tangent curvature vanishes and the metric satisfies some curvature conditions or have no conjugate points.     

具有相对迷向平均Landsberg曲率的流形的一个整体刚性定理

讨论了具有相对迷向平均Landsberg曲率的度量的一些几何性质.证明了任一闭的具有负旗曲率与相对迷向平均Landsberg曲率的流形一定是Riemann流形.     

Finsler metrics with constant （or scalar） flag curvature

A Finsler metric on a manifold M with its flag curvature K is said to be almost isotropic flag curvature if K =3c + σ where σ and c are scalar functions on M.In this paper,we establish the intrinsic re...     

关于射影平坦Finsler空间

本文研究了射影平坦Finsler空间的几何量及其几何性质。证明了射影平坦Finsler空间的Ricci曲率可完全由射影因子简洁地刻画出来。同时还证明了，在射影平坦Finsler空间中，平均Berwald曲率S=0意味着Ricci曲率Ric是二次齐次的。此外，给出了一个射影平坦Finsler空间成为常曲率空间或局部Minkowski空间的充分条件。     

Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below

We obtain the Laplacian comparison theorem and the Bishop-Gromov comparison theorem on a Finsler manifold with the weighted Ricci curvature Ric_∞ bounded below. As applications, we prove that if the weighted Ricci curvature Ric_∞ is bounded below by a positive number, then the manifold must have finite fundamental group, and must be compact if the distortion is also bounded. Moreover, we give the Calabi-Yau linear volume growth theorem on a Finsler manifold with nonnegative weighted Ricci curvature.     

Formulas of Gauss-Ostrogradskii Type on Real Finsler Manifolds

This article generalizes the formulas of Gauss-Ostrogradskii type for semibasic vector fields from Riemannian manifolds to real Finsler manifolds and obtains some formulas of Gauss-Ostrogradskii type for Finsler vector fields which are expressed in terms of the vertical and horizontal derivatives of the Cartan connection in real Finsler manifolds.     

一类浸入在半黎曼卷积空间的完备超曲面

We deal with complete hypersurfaces immersed in a semi-Riemannian warped product of the type eI×f M~n,where M~n is a connected n-dimensional oriented Riemannian manifold.When the fiber M~n is complete with sectional curvature-k≤K_M for some positive constant k,under appropriate restrictions on the norm of the gradient of the height function h,we proceed with our technique in order to guarantee that complete hypersurface immersed in a semi-Riemannian warped product is a slice.Our approach is based on the well known generalized maximum principle and another suitable maximum principle at the infinity due to Yau.     

Contact CR-Warped Product Submanifolds in Sasakian Manifolds

Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. The equality case is considered. Also, the minimum codimension of a contact CR-warped product in an odd-dimensional sphere is determined.     

On doubly warped product Finsler manifolds

In this paper, we introduce horizontal and vertical warped product Finsler manifolds. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemannian curvatures of doubly warped product Finsler manifold and its components, and consider the cases that this manifold is flat or has scalar flag curvature. We define the doubly warped Sasaki-Matsumoto metric for warped product manifolds and find a condition under which the horizontal and vertical tangent bundles are totally geodesic. We obtain some conditions under which a foliated manifold reduces to a Reinhart manifold. Finally, we study an almost complex structure on the tangent bundle of a doubly warped product Finsler manifold.     

射影平坦Finsler度量的解析构造

利用Hamel关于射影平坦的基本方程,我们导出了Randers度量的λ形变保持射影平坦的充分条件.特别,对一类具有特殊旗曲率性质的Randers度量我们证明了这类度量一定存在保持射影平坦性的λ形变.     

A note on the fundamental group of Finsler manifolds with nonnegative flag curvature

In this note we prove that the fundamental group of any forward complete Finsler manifold with nonnegative flag curvature is finitely generated provided the line integral of T-curvature is small. In particular, the fundamental group of any forward complete Berwald manifold with nonnegative flag curvature is finitely generated.     

Spacelike Graphs with Parallel Mean Curvature in Pseudo-Riemannian Product Manifolds

The author introduces the w-function defined on the considered spacelike graph M.Under the growth conditions w = o(log z) and w = o(r),two Bernstein type theorems for M in Rmn+ mare got,where z and r are the pseudo-Euclidean distance and the distance function on M to some fixed point respectively.As the ambient space is a curved pseudoRiemannian product of two Riemannian manifolds(Σ1,g1) and(Σ2,g2) of dimensions n and m,a Bernstein type result for n = 2 under some curvature conditions on Σ1 and Σ2 and the growth condition w = o(r) is also got.As more general cases,under some curvature conditions on the ambient space and the growth condition w = o(r) or w = o(√r),the author concludes that if M has parallel mean curvature,then M is maximal.