ON (α, β)-METRICS OF CONSTANT FLAG CURVATURE

doi:10.1007/s10473-022-0220-y

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 755-768.doi: 10.1007/s10473-022-0220-y

ON (α, β)-METRICS OF CONSTANT FLAG CURVATURE

陈光祖¹, 程新跃²

1. School of Science, East China JiaoTong University, Nanchang 330013, China;
2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

收稿日期:2020-11-18 修回日期:2021-02-22 出版日期:2022-04-25 发布日期:2022-04-22
通讯作者: Xinyue CHENG,E-mail:chengxy@cqnu.edu.cn E-mail:chengxy@cqnu.edu.cn
作者简介:Guangzu CHEN,E-mail:chenguangzu1@163.com
基金资助:
The second author is supported by the National Natural Science Foundation of China (11871126) and the Science Foundation of Chongqing Normal University (17XLB022).

ON (α, β)-METRICS OF CONSTANT FLAG CURVATURE

Guangzu CHEN¹, Xinyue CHENG²

1. School of Science, East China JiaoTong University, Nanchang 330013, China;
2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received:2020-11-18 Revised:2021-02-22 Online:2022-04-25 Published:2022-04-22
Supported by:
The second author is supported by the National Natural Science Foundation of China (11871126) and the Science Foundation of Chongqing Normal University (17XLB022).

摘要/Abstract

摘要： In this paper, we study the (α, β)-metrics of constant flag curvature. We characterize almost regular (α, β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to α. Furthermore, we prove that if a regular (α, β)-metric is of constant flag curvature and β is a Killing 1-form with constant length, then it must be a Riemannian metric or locally Minkowskian.

关键词: (α, β)-metric, flag curvature, S-curvature, mean Landsberg curvature, Riemannian metric, Minkowski metric, homothetic 1-form

Abstract: In this paper, we study the (α, β)-metrics of constant flag curvature. We characterize almost regular (α, β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to α. Furthermore, we prove that if a regular (α, β)-metric is of constant flag curvature and β is a Killing 1-form with constant length, then it must be a Riemannian metric or locally Minkowskian.

Key words: (α, β)-metric, flag curvature, S-curvature, mean Landsberg curvature, Riemannian metric, Minkowski metric, homothetic 1-form

中图分类号:

53B40

陈光祖, 程新跃. ON (α, β)-METRICS OF CONSTANT FLAG CURVATURE[J]. 数学物理学报(英文版), 2022, 42(2): 755-768.

Guangzu CHEN, Xinyue CHENG. ON (α, β)-METRICS OF CONSTANT FLAG CURVATURE[J]. Acta mathematica scientia,Series B, 2022, 42(2): 755-768.

ON (α, β)-METRICS OF CONSTANT FLAG CURVATURE

ON (α, β)-METRICS OF CONSTANT FLAG CURVATURE

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