On spaces with non-symmetric affine connection, containing subspaces without torsion

摘要

In the works by Minčič et al. (1998, 1999, 2007) [8], [9], [11] we have studied the problem (started by M. Prvanović): Can a generalized Riemannian space GRN (with non-symmetric basic tensor) contain a Riemannian subspace (possessing a symmetric induced basic tensor)?In the present work the analogous problem is studied for a space LN with non-symmetric affine connection and its subspace LM. In the Section 2 it is assumed that the equations defining submanifold are given and that it is valid (2.4), i.e., induced torsion T∼=0, and the connection on the manifold MN is determined so that T≠0. At the third section we start from connection on the manifold MNT≠0. From the mentioned condition (2.4) we determine the Eq. (1.1) defining the submanifold MM⊂MN, so that induced torsion T∼=0, i.e., we get LMO⊂LN.It is proved that the answer to the question cited above is affirmative and several examples are constructed. The examinations have local character.