ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

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

Abstract

Abstract:

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.

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

CLC Number:

53C60

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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