On a symmetric tensor field in areal space of submetric class

Abstract

The theory of isotropic areal space of submetric class was studied by Kawaguchi and Tandai (1952), Kikuchi (1968) and others . A symmetric curvature tensor field was defined and studied by the present author (1993) in generalized Finsler space. S.M.Uppal and the author (1996) have obtained Veblen identities in special Kawaguchi space . The purpose of the present paper is to define a symmetric tensor field and obtain its Bianchi and Veblen identities . The recurrence property of this tensor is dealt with in the last section of this paper .