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1.
In this paper, we study a class of Finsler metrics defined by a vector field on a Riemannian space form. We give an explicit formula for those with isotropic S-curvature. This class contains all Randers metrics of constant flag curvature. 相似文献
2.
Shin-ichi Ohta 《Differential Geometry and its Applications》2011,29(2):174-178
We give a necessary and sufficient condition on a Randers space for the existence of a measure for which Shen?s S-curvature vanishes everywhere. Moreover, if it exists, such a measure coincides with the Busemann-Hausdorff measure up to a constant multiplication. 相似文献
3.
We prove that a homogeneous Einstein–Randers space with negative Ricci curvature must be Riemannian. To cite this article: S. Deng, Z. Hou, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
4.
The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler metric with negative flag curvature and constant S-curvature must be Riemannian if the manifold is compact. We also study the nonpositive flag curvature case.supported by the National Natural Science Foundation of China (10371138). 相似文献
5.
Projectively flat Randers metrics with constant flag curvature 总被引:2,自引:0,他引:2
Zhongmin Shen 《Mathematische Annalen》2003,325(1):19-30
We classify locally projectively flat Randers metrics with constant Ricci curvature and obtain a new family of Randers metrics
of negative constant flag curvature.
Received: 19 July 2001 / Revised version: 15 March 2002 / Published online: 16 October 2002 相似文献
6.
Colleen Robles 《Transactions of the American Mathematical Society》2007,359(4):1633-1651
Geodesics in Randers spaces of constant curvature are classified.
7.
We give a survey on 4-dimensional manifolds with positive isotropic curvature. We will introduce the work of B. L. Chen, S. H. Tang and X. P. Zhu on a complete classification theorem on compact four-manifolds with positive isotropic curvature (PIC). Then we review an application of the classification theorem, which is from Chen and Zhu’s work. Finally, we discuss our recent result on the path-connectedness of the moduli spaces of Riemannian metrics with positive isotropic curvature. 相似文献
8.
We showed that any reversible Finsler metric with positive constant flag curvature must be Riemannian.
Received: 18 August 2008 相似文献
9.
Annals of Global Analysis and Geometry - The critical point equation arises as a critical point of the total scalar curvature functional defined on the space of constant scalar curvature metrics of... 相似文献
10.
In the paper we prove the path-connectedness of the moduli spaces of metrics with positive isotropic curvature on certain compact four-dimensional manifolds. 相似文献
11.
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
12.
M.-L. Labbi 《Proceedings of the American Mathematical Society》2000,128(5):1467-1474
In this paper we construct new Riemannian metrics with positive isotropic curvature on compact manifolds which fiber over the circle. We also study the relationship between the positivity of the isotropic curvature and the positivity of the -curvature.
13.
We prove that every locally connected quotient G/H of a locally compact, connected, first countable topological group G by
a compact subgroup H admits a G-invariant inner metric with curvature bounded below. Every locally compact homogeneous space
of curvature bounded below is isometric to such a space. These metric spaces generalize the notion of Riemannian homogeneous
space to infinite dimensional groups and quotients which are never (even infinite dimensional) manifolds. We study the geometry
of these spaces, in particular of non-negatively curved homogeneous spaces.
Dedicated to the memory of A. D. Alexandrov 相似文献
14.
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
15.
A class of Finsler metrics with isotropic S-curvature 总被引:3,自引:0,他引:3
In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form. We characterize these metrics
with isotropic S-curvature.
Supported by a NNSFC grant (10671214) and by the NSF project of CQ CSTC.
Supported by a NNSFC grant (10671214), a NSF grant (DMS-0810159) and the C. K. Chao Foundation for Advanced Research 相似文献
16.
17.
In this paper, we study a class of Finsler metrics defined by a Riemannian metric and 1-form. We classify those metrics which are projectively flat with weakly isotropic flag curvature. 相似文献
18.
V. N. Berestovskii 《Mathematical Notes》1995,58(3):905-909
We prove that a homogeneous effective spaceM=G/H, whereG is a connected Lie group andH⊂G is a compact subgroup, admits aG-invariant Riemannian metric of positive Ricci curvature if and only if the spaceM is compact and its fundamental group π1(M) is finite (in this case any normal metric onG/H is suitable). This is equivalent to the following conditions: the groupG is compact and the largest semisimple subgroupLG⊂G is transitive onG/H. Furthermore, ifG is nonsemisimple, then there exists aG-invariant fibration ofM over an effective homogeneous space of a compact semisimple Lie group with the torus as the fiber.
Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 334–340, September, 1995. 相似文献
19.
《Differential Geometry and its Applications》2001,14(1):57-78
We calculate the full isometry group in the case G/H admits a homogeneous metric of positive sectional curvature. 相似文献