On the ME-manifold in n-*g-UFT and its conformal change

Abstract

An Einstein's connection which takes the form (3.1) is called an ME-connection. A generalized n-dimensional Riemannian manifold Xn on which the differential geometric structure is imposed by a tensor field *gλν through a unique ME-connection subject to the conditions of Agreement (4.1) is called *g-ME-manifold and we denote it by *g-MEXn. The purpose of the present paper is to introduce this new concept of *g-MEXn and investigate its properties. In this paper, we first prove a necessary and sufficient condition for the unique existence of ME-connection in Xn, and derive a surveyable tensorial representation of the ME-connection. In the second, we investigate the conformal change of *g-MEXn and present a useful tensorial representation of the conformal change of the ME-connection.

Keywords

• *g-MEXn
• ME-connection
• ME-vector
• conformal change.