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

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Hagia Sophia Journal of Geometry
Volume:1 Issue:1
Weingarten Map of the Hypersurface in Euclidean 4-Space and its Applications

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

Authors : Salim YÜCE

Pages : 1-8

View : 49 | Download : 10

Publication Date : 2019-02-05

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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

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