Theory of Hypersurfaces yn–1 in yn Space and Geodesics on this Hypersurfaces yn–1

Abstract

The hypersurface yn–1 in yn space is studied for this piece of work. We established the correlation between tensors of hypersurface yn–1 and tensors of embedding space yn . The second non-symmetrical tensor of hypersurface has been introduced, which have been obtained from the analog of Peterson-Codazzi equation in nonsymmetrical case.Also we have introduced the tensor that is associated with square of angle between normal and adjacent normal and it is represented in terms of metric and second tensors of hypersurface. The geodesics on hypersurface have been studied, and nontrivial example of geodesics on hypersurface with torsion and Euclid metric was constructed.