共查询到20条相似文献,搜索用时 31 毫秒
1.
Every Finsler metric induces a spray on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called the projective Ricci curvature. The projective Ricci curvature is an important projective invariant in Finsler geometry. In this paper, we study and characterize projectively Ricci-flat square metrics. Moreover, we construct some nontrivial examples on such Finsler metrics. 相似文献
2.
关于射影平坦Finsler空间 总被引:4,自引:0,他引:4
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。 相似文献
3.
标量曲率Finsler空间与Finsler度量的射影变换 总被引:1,自引:0,他引:1
本文研究了与一个Ricci平坦Finsler空间或一个常曲率Finsler空间射影相关的标量曲率Finsler空间.我们给出了这种标量曲率Finsler空间成为常曲率空间的充分必要条件.特别地,我们给出了射影平坦Finsler空间具有常曲率的条件. 相似文献
4.
Songting YIN 《Frontiers of Mathematics in China》2018,13(2):435-448
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. 相似文献
5.
《中国科学 数学(英文版)》2020,(7)
One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant(or scalar) curvature. In this paper, we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metrics of scalar flag curvature. In particular, we find equations that characterize Finsler warped product metrics of constant flag curvature. Then we improve the Chen-Shen-Zhao result on characterizing Einstein Finsler warped product metrics. As its application we construct explicitly many new warped product Douglas metrics of constant Ricci curvature by using known locally projectively flat spherically symmetric metrics of constant flag curvature. 相似文献
6.
In this paper, we investigate the flag curvature of a special class of Finsler metrics called general spherically symmetric Finsler metrics, which are defined by a Euclidean metric and two related 1-forms. We find equations to characterize the class of metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover, we study general spherically symmetric Finsler metrics with the vanishing non-Riemannian quantity χ-curvature. In particular, we construct some new projectively flat Finsler metrics of constant flag curvature. 相似文献
7.
Yau made the following conjecture: For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional. we extend the result on the Laplace operator to that on the symmetric diffusion operator, and prove the space of L-harmonic functions with polynomial growth of a fixed rate is finite-dimensional, when m-dimensional Bakery-Emery Ricci curvature of the symmetric diffusion operator on the complete noncompact Riemannian manifold is nonnegative. 相似文献
8.
In this paper, we study the integrals of the Ricci curvature over metric balls in a Finsler manifold,which can be viewed as an L~q-norm of the Ricci curvature. By bounding such integrals from above, we obtain several Myers type theorems. 相似文献
9.
Finsler空间上的Weyl曲率 总被引:1,自引:0,他引:1
MoXiaohuan 《高校应用数学学报(英文版)》2005,20(1):10-20
The Weyl curvature of a Finsler metric is investigated. This curvature constructed from Riemannain curvature. It is an important projective invariant of Finsler metrics. The author gives the necessary conditions on Weyl curvature for a Finsler metric to be Randers metric and presents examples of Randers metrics with non-scalar curvature. A global rigidity theorem for compact Finsler manifolds satisfying such conditions is proved. It is showed that for such a Finsler manifold,if Ricci scalar is negative,then Finsler metric is of Randers type. 相似文献
10.
In this paper, we study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. When the Ricci curvature
is nonnegative, we show that this kind of manifolds are diffeomorphic to a Euclidean space, by assuming an upper bound on
the radial curvature and a volume growth condition of their geodesic balls. When the Ricci curvature only has a lower bound,
we also prove that such a manifold is diffeomorphic to a Euclidean space if the radial curvature is bounded from below. Moreover,
by assuming different conditions and applying different methods, we shall prove more results on Riemannian manifolds with
large volume growth. 相似文献
11.
Yau made the following conjecture: For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic
functions with polynomial growth of a fixed rate is finite dimensional. we extend the result on the Laplace operator to that
on the symmetric diffusion operator, and prove the space of L-harmonic functions with polynomial growth of a fixed rate is finite-dimensional, when m-dimensional Bakery-Emery Ricci curvature of the symmetric diffusion operator on the complete noncompact Riemannian manifold
is nonnegative. 相似文献
12.
We establish existence and uniqueness theorems for V-harmonic maps from complete noncompact manifolds. This class of maps includes Hermitian harmonic maps, Weyl harmonic maps, affine harmonic maps, and Finsler harmonic maps from a Finsler manifold into a Riemannian manifold. We also obtain a Liouville type theorem for V-harmonic maps. In addition, we prove a V-Laplacian comparison theorem under the Bakry-Emery Ricci condition. 相似文献
13.
14.
Xiaohuan Mo 《中国科学A辑(英文版)》1998,41(9):910-917
The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved
that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curvature along the Hilbert form on
the projective sphere bundle attains identically its maximum (resp. Ricci scalar). The horizontal distributionH of this bundle is integrable if and only ifM has zero flag curvature. When a Finsler space has CFC, Hilbert form’s orthogonal complement in the horizontal distribution
is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and
its first normal space is vertical
Project supported by Wang KC Fundation of Hong Kong and the National Natural Science Foundation of China (Grant No. 19571005). 相似文献
15.
Bing Ye Wu 《Proceedings Mathematical Sciences》2014,124(3):411-417
In this paper, an upper bound on the growth of fundamental group for a class of Finsler manifolds with integral Ricci curvature bound is given. This generalizes the corresponding results with pointwise Ricci curvature in literature. 相似文献
16.
17.
Xiaohuan MO 《Frontiers of Mathematics in China》2011,6(2):309-323
The purpose of this article is to derive an integral inequality of Ricci curvature with respect to Reeb field in a Finsler
space and give a new geometric characterization of Finsler metrics with constant flag curvature 1. 相似文献
18.
芬斯勒射影几何中的Ricci曲率 总被引:1,自引:1,他引:0
本文研究了保持Ricci曲率不变的Finsler射影变换。给定一个紧致无边的n维可微流形M,证明了:对于一个从M上的Berwald度量到Riemann度量的C-射影变换,如果Berwald度量的Ricci曲率关于Riemann度量的迹不超过Riemann度量的标量曲率,则该射影变换是平凡的。 相似文献
19.
We show that recent work of Ni and Wilking (in preparation) [11] yields the result that a noncompact nonflat Ricci shrinker has at most quadratic scalar curvature decay. The examples of noncompact Kähler–Ricci shrinkers by Feldman, Ilmanen, and Knopf (2003) [7] exhibit that this result is sharp. We also prove a similar result for certain noncompact steady gradient Ricci solitons. 相似文献
20.
Liang Ming Shen 《数学学报(英文版)》2015,31(9):1391-1414
In this paper, we study Ricci flow on noncompact 4-manifolds with uniformly positive isotropic curvature and with no essential imcompressible space form. That means there is positive lower bound of isotropic curvature and bounded geometry. Then by Perelman's technique, we can analyze the structures of such manifolds. 相似文献