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

Year 2019, Volume: 1 Issue: 1, 1 - 8, 05.02.2019

Salim Yüce

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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