具有零旗曲率的 Landsberg 芬斯勒卷积度量

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1831-1842.

具有零旗曲率的 Landsberg 芬斯勒卷积度量

郑大小()

安徽师范大学安徽芜湖 241002

收稿日期:2022-08-30 修回日期:2022-12-30 出版日期:2023-12-26 发布日期:2023-11-16
作者简介:郑大小，E-mail: 2015046@ahnu.edu.cn
基金资助:
安徽省自然科学青年基金(2008085QA05)

Landsberg Finsler Warped Product Metrics with Zero Flag Curvature

Zheng Daxiao()

Department of Mathematics and Statistics Science, Anhui Normal University, Anhui Wuhu 241002

Received:2022-08-30 Revised:2022-12-30 Online:2023-12-26 Published:2023-11-16
Supported by:
Anhui Provincial Natural Science Youth Foundation(2008085QA05)

摘要/Abstract

摘要：

该文研究芬斯勒卷积度量, 得到了 Landsberg 芬斯勒卷积度量的方程刻画, 并且完全求解出了方程. 在此基础上, 构造了一类非 Berwald 且具有零旗曲率的 Landsberg 芬斯勒卷积度量.

关键词: 芬斯勒卷积度量, Douglas张量, 旗曲率张量, Landsberg曲率

Abstract:

In this paper, we study Finsler warped product metrics. We obtain the differential equations that characterize Landsberg Finsler warped product metrics. By solving these equations, we obtain the expression of these metrics. Furthermore, we construct a class of Finsler warped product metrics $F$ with the following properties: $(1)$ $F$ is a Landsberg metric; $(2)$ $F$ is not a Berwald metric; $(3)$ $F$ has zero flag curvature (or Ricci curvature).

Key words: Finsler warped product metrics, Douglas metrics, Flag curvature, Landsberg

中图分类号:

O184

郑大小. 具有零旗曲率的 Landsberg 芬斯勒卷积度量[J]. 数学物理学报, 2023, 43(6): 1831-1842.

Zheng Daxiao. Landsberg Finsler Warped Product Metrics with Zero Flag Curvature[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1831-1842.

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