In this paper, results obtained by the author for Riemannian Spaces V n imbedded in Euclidean Spaces E N (3; 4) are extended to V n imbedded in V N . The first section is introductory. In §2 the general result is obtained. This is the establishment of a certain dependency among the three basic sets of equations of the V n with respect to the V N , namely the equations of Gauss, Codazzi and Kuehne. In §3 it is assumed that V N is of constant curvature with N = n + 1. This case is discussed with

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... he help of a generalization of the type number r introduced by Thomas (10) . Throughout the paper the conventional tensor notation has been adopted. Capital latin indices vary from 1 to N, small latin indices from 1 to n, and small greek indices from 1 to v = N -n. Whenever an index occurs twice in an expression, the summation with respect to that index has to be performed, except when otherwise stated. This summation convention is not restricted to indices with opposite (i.e. one of covariant and the other of contravariant) character. (III) K a @ I ij = t a $ \i,j -tap | j, i + (tya | ityfl | j ~ t ya | jt y p | f) +# (b a \ ki bfi\ij -b a \ k jbp\u) + RijKL^a^X ti X tj = 0.