On a class of two-dimensional Finsler manifolds of isotropic S-curvature

For an（α, β）-metric（non-Randers type） of isotropic S-curvature on an n-dimensional manifold with non-constant norm ‖β‖α, we first show that n = 2, and then we characterize such a class of two-dimensional（α, β）-manifolds with some PDEs, and also construct some examples for such a class....

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Bibliographic Details
Published inScience China. Mathematics Vol. 61; no. 1; pp. 57 - 72
Main Authors Cheng, Xinyue, Shen, Zhongmin, Yang, Guojun
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 2018
Springer Nature B.V
Subjects
Applications of Mathematics
Curvature
Mathematics
Mathematics and Statistics
(
53B40
S-curvature
,
metric
Randers metric
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Summary:For an（α, β）-metric（non-Randers type） of isotropic S-curvature on an n-dimensional manifold with non-constant norm ‖β‖α, we first show that n = 2, and then we characterize such a class of two-dimensional（α, β）-manifolds with some PDEs, and also construct some examples for such a class.
Bibliography:（α,β）-metric Randers metric S-curvature
For an（α, β）-metric（non-Randers type） of isotropic S-curvature on an n-dimensional manifold with non-constant norm ‖β‖α, we first show that n = 2, and then we characterize such a class of two-dimensional（α, β）-manifolds with some PDEs, and also construct some examples for such a class.
11-5837/O1
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-016-9079-1