Transilvania University of Brasov
Abstract: In this paper, we endow the holomorphic tangent bundle with a generalized Sasaki type lift $G$ of the fundamental metric tensor of a complex Finsler space. In order to build the Einstein equations on the holomorphic tangent bundle, we determine the Levi-Civita complex linear connection corresponding to this metric. As an application, we give some solutions of the complex Einstein equations in a weakly gravitational space.
Keywords: Holomorphic tangent bundle, Chern-Finsler connection, complex Einstein equations.
Classification (MSC2000): 53B40; 53C60
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