ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

doi:10.1016/S0252-9602(16)30103-5

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (6): 1747-1766.doi: 10.1016/S0252-9602(16)30103-5

ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

何勇^1,2, 钟春平¹

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830053, China

收稿日期:2015-05-11 修回日期:2015-12-22 出版日期:2016-12-25 发布日期:2016-12-25
作者简介:Yong HE,E-mail:19020130154147@stu.xmu.edu.cn;Chunping ZHONG,E-mail:zcp@xmu.edu.cn
基金资助:
This work is supported by Program for New Century Excellent Talents in University (NCET-13-0510); National Natural Science Foundation of China (11271304, 11571288, 11461064); the Fujian Province Natural Science Funds for Distinguished Young Scholar (2013J06001); the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

Yong HE^1,2, Chunping ZHONG¹

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830053, China

Received:2015-05-11 Revised:2015-12-22 Online:2016-12-25 Published:2016-12-25
Supported by:
This work is supported by Program for New Century Excellent Talents in University (NCET-13-0510); National Natural Science Foundation of China (11271304, 11571288, 11461064); the Fujian Province Natural Science Funds for Distinguished Young Scholar (2013J06001); the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

摘要/Abstract

摘要：

Let (M₁,F₁) and (M₂,F₂) be two strongly pseudoconvex complex Finsler manifolds. The doubly wraped product complex Finsler manifold (_f₂M₁×_f₁M₂, F) of (M₁, F₁) and (M₂, F₂) is the product manifold M₁×M₂ endowed with the warped product complex Finsler metric F₂=f₂²F₁²+f₁²F₂², where f₁ and f₂ are positive smooth functions on M₁ and M₂, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be Kähler Finsler (resp., weakly Kähler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg) manifold are obtained, respectively. It is proved that if (M₁, F₁) and (M₂, F₂) are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if f₁ and f₂ are positive constants.

关键词: doubly warped products, complex Finsler metric, holomorphic curvature, geodesic

Abstract:

Key words: doubly warped products, complex Finsler metric, holomorphic curvature, geodesic

中图分类号:

53C60

何勇, 钟春平. ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS[J]. 数学物理学报(英文版), 2016, 36(6): 1747-1766.

Yong HE, Chunping ZHONG. ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS[J]. Acta mathematica scientia,Series B, 2016, 36(6): 1747-1766.

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ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

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