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An Einstein's connection which takes the form (2.23) is called a ∗g-M E-connection and the corresponding vector is called a ∗g-M E-vector. The ∗g-M E-manifold is a generalized n-dimensional Riemannian manifold Xn on which the differential geometric structure is imposed by the unified field tensor ∗gλν , satisfying certain conditions, through the ∗g-M Econnection and we denote it by ∗g-M EXn. The purpose of this paper is to derive a general representation and a special representation of the ∗g-M Evector in ∗g-M EXn.
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