Weingarten Map of the Hypersurface in Euclidean 4-Space and its Applications

Abstract

In this paper, by taking into account the beginning of the hypersurface theory in Euclidean space E 4 , a practical method for the matrix of the Weingarten map (or the shape operator) of an oriented hypersurface M3 in E 4 is obtained. By taking this efficient method, it is possible to study of the hypersurface theory in E 4 which is analog the surface theory in E 3 . Furthermore, the Gaussian curvature, Mean curvature, fundamental forms and Dupin indicatrix of M3 is introduced.

Keywords

• Shape operator,vector product,ternary product,Dupin indicatrix,Weingarten Map

References

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