Integrability conditions of derivational equations of a submanifold of a generalized Riemannian space

摘要

The basic information on generalized Riemannian space GRN and its submanifold XM and normal bundle XN-MN are given. As introduced connections are generally asymmetric, it is possible to define four kinds of covariant derivative.In the present work one considers integrability conditions of derivational equations obtained by using the 1st and the 2nd kind of covariant derivative. We obtain also the corresponding Gauss–Codazzi equations. Similar results using simultaneously the both kinds of covariant derivative are obtained.