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 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 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: 12) 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: 12) metrichomogeneous Finsler space, naturally reductive, S-curvature