On curvatures of spaces with normal general connections. II.

Abstract

In this paper, the author makes a formula (§ 2) related to the curvature tensors of a normal general connection γ and BγB, where B is a tensor field of type (1, 1) satisfying some conditions, making use of the results in a previous paper [14], and then he shows that the formula applied to the case in which γ is a classical affine connection is a generalization of the Gauss' equations in the theory of subspaces of Riemannian geometry (§4). He also shows that regarding the set of general connections as a vector space over the algebra of all tensor fields of type (1, 1), the calculations in connection with the above purpose can be simplified.