On Doubly Twisted Product of Complex Finsler Manifolds

IF 0.8 4区 数学 数学研究 Pub Date : 2022-06-01 DOI:10.4208/jms.v55n2.22.04
W. Xiao, Yong He, Xiaoying Lu null, Xiangxiang Deng
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引用次数: 4

Abstract

Let (M1,F1) and (M2,F2) be two strongly pseudoconvex complex Finsler manifolds. The doubly twisted product (abbreviated as DTP) complex Finsler manifold (M1×(λ1,λ2) M2,F) is the product manifold M1×M2 endowed with the twisted product complex Finsler metric F=λ1F 2 1 +λ 2 2F 2 2 , where λ1 and λ2 are positive smooth functions on M1×M2. 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. AMS subject classifications: 53C60, 53C40
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复Finsler流形的双扭积
设(M1,F1)和(M2,F2)是两个强拟凸复Finsler流形。双扭积(简称DTP)复Finsler流形(M1×(λ1,λ2)M2,F)是被赋予扭积复Finsler-度量F=λ1F2 1+λ2F2 2的乘积流形M1×M2,其中λ1和λ2是M1×M2上的正光滑函数。本文导出了DTP复Finsler流形的几何对象(如复Finsleer连接、全纯和Ricci标量曲率以及实测地线)与其分量之间的关系。得到了DTP复Finsler流形是Kähler-Finsler(分别为弱Käler-Finsler,复Berwald,弱复Berwal,复Landsberg)流形的充要条件。通过这些,我们提供了一种构造弱复Berwald流形的可能方法,然后给出了不是Berwald度量的复Landsberg度量的特征。AMS科目分类:53C60、53C40
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数学研究
数学研究 MATHEMATICS-
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