DECOMPOSITION FOR CARTAN’S SECOND CURVATURE TENSOR OF DIFFERENT ORDER IN FINSLER SPACES

Abstract

The Cartan’s second curvature tensor P^i_{jkh} is a positively homogeneous of degree-1 in y^i, where yi represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan’s second curvature tensor P^i_{jkh} in two spaces, a generalized BP-recurrent space and generalized BP-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.