Showing papers by "Uday Chand De published in 1989"

On pseudo symmetric spaces

Abstract: where 21 is a non-zero vector and comma denotes covariant differentiation with respect to the metric tensor of the space. Such a space was called by him a pseudo symmetric space and 2t was called its associated vector. An n-space of this kind was denoted by (PS),. The name pseudo symmetric was chosen, because if in (1) 2t is taken as zero, then the equation (1) takes the form Rhijk.t=0 and the space reduces to a symmetric space in the sense of Caftan. In the present paper some results on a (PS), are established. In Section 3 it is shown that if a (PS), is a decomposable space V~• (r_->2, n-r>=2), then one of the decomposition spaces is flat and the other is a pseudo symmetric space. In Section 4 the Ricci-associate of the vector field 21 is defined and some theorems relating to it are proved. Section 5 deals with (PS), (n>3) having cyclic Ricci tensor. The last section is concerned with (PS), admitting a concurrent or a recurrent vector field [4].