On Generalized Riemannian Spaces Containing Riemannian Subspaces

In the paper, we establish conditions under which a generalized Riemannian space may contain a subspace with symmetric induced basic tensor. We consider the two cases. In the first case, a subspace is assumed to be given, and the problem is to find the skew-symmetric part of the basic tensor of the space. In the second case, the skew-symmetric part of the basic tensor is given, and the problem is to find a subspace such that the induced basic tensor is symmetric. All results are local in character.