数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (4): 1547-1560.doi: 10.1007/s10473-023-0406-y

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NATURALLY REDUCTIVE (α1, α2) METRICS∗

Ju TAN1, Ming XU2,†   

  1. 1. School of Microelectronics and Data Science, Anhui University of Technology, Maanshan 243032, China;
    2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 收稿日期:2022-04-18 修回日期:2022-10-17 出版日期:2023-08-08 发布日期:2023-08-08
  • 通讯作者: †Ming XU, E-mail: mgmgmgxu@163.com
  • 作者简介:Ju TAN, E-mail: tanju2007@163.com
  • 基金资助:
    *National Natural Science Foundation of China (12131012, 12001007, 11821101), the Beijing Natural Science Foundation (1222003, Z180004) and the Natural Science Foundation of Anhui province (1908085QA03).

NATURALLY REDUCTIVE (α1, α2) METRICS∗

Ju TAN1, Ming XU2,†   

  1. 1. School of Microelectronics and Data Science, Anhui University of Technology, Maanshan 243032, China;
    2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • Received:2022-04-18 Revised:2022-10-17 Online:2023-08-08 Published:2023-08-08
  • Contact: †Ming XU, E-mail: mgmgmgxu@163.com
  • About author:Ju TAN, E-mail: tanju2007@163.com
  • Supported by:
    *National Natural Science Foundation of China (12131012, 12001007, 11821101), the Beijing Natural Science Foundation (1222003, Z180004) and the Natural Science Foundation of Anhui province (1908085QA03).

摘要: Letting $F$ be a homogeneous $(\alpha_1,\alpha_2)$ metric on the reductive homogeneous manifold $G/H$, we first characterize the natural reductiveness of $F$ as a local $f$-product between naturally reductive Riemannian metrics. Second, we prove the equivalence among several properties of $F$ for its mean Berwald curvature and S-curvature. Finally, we find an explicit flag curvature formula for $G/H$ when $F$ is naturally reductive.

关键词: (α1,α2) metrichomogeneous Finsler space, naturally reductive, S-curvature

Abstract: Letting $F$ be a homogeneous $(\alpha_1,\alpha_2)$ metric on the reductive homogeneous manifold $G/H$, we first characterize the natural reductiveness of $F$ as a local $f$-product between naturally reductive Riemannian metrics. Second, we prove the equivalence among several properties of $F$ for its mean Berwald curvature and S-curvature. Finally, we find an explicit flag curvature formula for $G/H$ when $F$ is naturally reductive.

Key words: (α1,α2) metrichomogeneous Finsler space, naturally reductive, S-curvature