The Gauss Map and the Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space

Symmetry

YoungHo Kim¹  Erhan Güler²  HasanHilmi Hacısalihoğlu³ 

[1] Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea;Faculty of Sciences, Department of Mathematics, Bartın University, Bartın 74100, Turkey;Faculty of Sciences, Department of Mathematics, Şeyh Edebali University (Emeritus), Bilecik 11230, Turkey;

关键词: four-space;    rotational hypersurface;    Gauss map;    Gaussian curvature;    mean curvature;    the third Laplace–Beltrami operator;   

DOI  :  10.3390/sym10090398

来源: DOAJ

【 摘 要 】

We study and examine the rotational hypersurface and its Gauss map in Euclidean four-space E 4. We calculate the Gauss map, the mean curvature and the Gaussian curvature of the rotational hypersurface and obtain some results. Then, we introduce the third Laplace–Beltrami operator. Moreover, we calculate the third Laplace–Beltrami operator of the rotational hypersurface inE 4. We also draw some figures of the rotational hypersurface.

【 授权许可】

Unknown