Differential Geometry Of Hypersurfaces Of N-dimensional Euclidean Spaces

The differential geometry of surfaces of 3 dimensional Euclidean spaces is a subject that discusses the geometrical properties of the surfaces, and has important applications in theoretical as well as practical. In this paper, we investigate systematically the differential geometry of hypersurfaces of n dimensional Euclidean spaces, such as the first and the second fundamental forms, the curvature tensors, the Gaussian equations, the Gaussian theorem and the fundamental theorem of hypersurfaces, and generalize the differential geometry of surfaces.