Recently, Chung and et al. ([11], 1991c) introduced a new concept of a manifold, denoted by ＊g-SE

, in Einstein's n-dimensional ＊g-unified field theory. The manifold ＊g-SE

is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor ＊

through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor ＊

. This paper is the first part of the following series of two papers: I. The SE-curvature tensor of ＊g-SE

II. The contracted SE-curvature tensors of ＊g-SE

In the present paper we investigate the properties of SE-curvature tensor of ＊g-SE

, with main emphasis on the derivation of several useful generalized identities involving it. In our subsequent paper, we are concerned with contracted curvature tensors of ＊g-SE

and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in ＊g-SE

, which has a great deal of useful physical applications.tions.