Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (2): 755-768.doi: 10.1007/s10473-022-0220-y

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Guangzu CHEN1, Xinyue CHENG2   

  1. 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).

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

CLC Number: 

  • 53B40