A Finsler Space with Conservative Berwald Curvature

Abstract

The present paper deals with a Finsler space with conservative Berwald curvature tensor. The condition characterizing such
space is weaker than the condition characterizing a symmetric Finsler space1, 2 . It is established that Berwald torsion tensor and deviation tensor of a Finsler space with conservative Berwaldcurvature tensor are conservative but the converse is true only when certain conditions are satisfied. Apart from establishing the symmetry of the covariant derivative B H h jk of Ricci tensor in the indices h and k and certain identities, it is proved that the projective curvature tensor of a Finsler space with conservative Berwald curvature tensor is conservative only when the tensor m k B H is symmetric.