Weingarten map of the hypersurface in 4-dimensional Euclidean space and its applications

2019/01/21 by Sali̇m Yüce, Yüce, Salim
Mathematics · #14Q10 #53A05 #53A07 #FOS: Mathematics #General Mathematics (math.GM) #Geometric Analysis and Curvature Flows #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1901.07883

openalex publication_date 2019/01/21 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

In this paper, by taking into account the beginning of the hypersurface theory in Euclidean space E⁴, a practical method for the matrix of the Weingarten map (or the shape operator) of an oriented hypersurface M³ in E⁴ is obtained. By taking this efficient method, it is possible to study of the hypersurface theory in E⁴ which is analog the surface theory in E³. Furthermore, the Gaussian curvature, mean curvature, fundamental forms and Dupin indicatrix of M³ is introduced.

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