Einstein equations of G-natural complex Finsler metrics

Szász, Annamária (2015) Einstein equations of G-natural complex Finsler metrics. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 31 (1). pp. 139-151. ISSN 0866-0174

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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.

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