Geodesic infinitesimal deformations of generalized Riemannian space

Abstract

Infinitesimal deformations of subspaces of a generalized Riemannian space are studied in this paper. Variations of some geometric objects are found. Necessary and sufficient conditions which provide the existence of a geodesic infinitesimal deformation of a generalized Riemannian space are obtained. Basic equations of a geodesic infinitesimal deformation such as a system of differential equations which determined an infinitesimal deformation field are given.