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 On the geometry of the manifold $MEX_{2n}$ Bull. Korean Math. Soc. 2003 Vol. 40, No. 3, 475-487 Published online September 1, 2003 Ki-Jo Yoo Mokpo National University Abstract : A generalized even-dimensional Riemannian manifold defined by the $ME$-connection which is both Einstein and of the form (3.3) is called an even-dimensional $ME$-manifold and we denote it by $MEX_{2n}$. The purpose of this paper is to study a necessary and sufficient condition that there is an $ME$-connection, to derive the useful properties of some tensors, and to investigate a representation of the $ME$-vector in $MEX_{2n}$. Keywords : $ME$-vector, $ME$-connection, $ME$-manifold, Einstein's equation MSC numbers : 53A30, 53C07, 53C25 Downloads: Full-text PDF