On Doubly Twisted Product of Complex Finsler Manifolds

On Doubly Twisted Product of Complex Finsler Manifolds

Year:    2022

Author:    Wei Xiao, Yong He, Xiaoying Lu, Xiangxiang Deng

Journal of Mathematical Study, Vol. 55 (2022), Iss. 2 : pp. 158–179

Abstract

Let $(M_1,F_1)$ and $(M_2,F_2)$ be two strongly pseudoconvex complex Finsler manifolds. The doubly twisted product (abbreviated as DTP) complex Finsler manifold $(M_1\times_{(\lambda_1,\lambda_2)}M_2,F)$ is the product manifold $M_1\times M_2$ endowed with the twisted product complex Finsler metric $F^2=\lambda_1^2F_1^2+\lambda_2^2F_2^2$, where $\lambda_1$ and $\lambda_2$ are positive smooth functions on $M_1\times M_2$. In this paper, the relationships between the geometric objects (e.g. complex Finsler connections, holomorphic and Ricci scalar curvatures, and real geodesic) of a DTP-complex Finsler manifold and its components are derived. The necessary and sufficient conditions under which the DTP-complex Finsler manifold is a Kähler Finsler (respctively weakly Kähler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg) manifold are obtained. By means of these, we provide a possible way to construct a weakly complex Berwald manifold, and then give a characterization for a complex Landsberg metric that is not a Berwald metric.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v55n2.22.04

Journal of Mathematical Study, Vol. 55 (2022), Iss. 2 : pp. 158–179

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Doubly twisted products complex Finsler metric holomorphic curvature geodesic.

Author Details

Wei Xiao

Yong He

Xiaoying Lu

Xiangxiang Deng

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