A Generalization of the Bonnet Theorem to the Parallel Submanifolds

Abstract

In this paper, we give a generalization of the Bonnet Theorem to parallel submanifolds in E^m. The Bonnet Theorem is well known for the parallel surfaces and parallel hypersurfaces as in [2],[3] . Finally, we obtain the Bonnet Theorem for the special cases of the parallel surfaces in E³ and the parallel hypersurfaces in E^m.