Locally Conformally Flat Doubly Twisted Product Complex Finsler Manifolds

Abstract

Let M 1 × λ 1 , λ 2 M 2 , F be a doubly twisted product manifold of two strongly pseudoconvex complex Finsler manifolds M 1 , F 1 and M 2 , F 2 . In this study, we give a characterization of locally conformally flat doubly twisted product complex Finsler manifold. We also obtain a necessary and sufficient condition for a doubly twisted product of two locally conformally flat complex Finsler manifolds to be locally conformally flat.

Levi-Civita Ricci-Flat Doubly Warped Product Hermitian Manifolds

“…They also gave the necessary and sufficient condition for a compact nontrivial DWP-Hermitian manifold to be of constant holomorphic sectional curvature. Recently, Xiao et al [16] systematically studied holomorphic curvatures of doubly twisted product complex Finsler manifolds, and they [17] gave the necessary and sufficient condition for doubly twisted product complex Finsler manifold to be locally dually flat.…”