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

A Finsler metric of a manifold or vector bundle is dened as asmooth assignment for each base point, a norm on each ber space and thusthe class of Finsler metrics contains Riemannian metrics as a special sub-class. The geometry of complex Finsler manifold has been developed by [7].In complex Finsler manifolds, the study of theory of curvatures has been anactive eld of research over past few decades. In the present article, our mainpurpose is to discuss some techniques of decomposition for the well knownCartan's rst curvature tensor Sijkh. Moreover, we attempted to establishfew signicant results that may produce vital connections between complexFinsler and complex Einstein's manifolds. Also, by adopting the techniquesof decomposition, various cases and conditions have been developed and theiradvantages in the study of theory of relativity & cosmology have been pursued.