Einstein's connection in 5-dimensional ES-manifold

Abstract

The manifold ${}^{\ast }g-ES{X}_n$ is a generalized $n$-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor ${}^{\ast }{g}^{\lambda \nu }$ through the $ES$-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in $5$-dimensional ${}^{\ast }g-ES{X}_5$ and to display a surveyable tnesorial representation of $5$-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.