TECHNIQUES FOR THE DECOMPOSITION OF CARTAN’S CURVATURE TENSOR IN COMPLEX FINSLER MANIFOLDS

Abstract

A Finsler metric of a manifold or vector bundle is defined as a smooth assignment for each base point, a norm on each fiber space and thus the class of Finsler metrics contains Riemannian metrics as a special subclass. The geometry of complex Finsler manifold has been developed by [7]. In complex Finsler manifolds, the study of theory of curvatures has been an active field of research over past few decades. In the present article, our main purpose is to discuss some techniques of decomposition for the well known Cartan’s first curvature tensor $S_{jkh}^i$. Moreover, we attempted to establish few significant results that may produce vital connections between complex Finsler and complex Einstein’s manifolds. Also, by adopting the techniques of decomposition, various cases and conditions have been developed and their advantages in the study of theory of relativity & cosmology have been pursued.