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Symmetry 2018, 10(9), 398; https://doi.org/10.3390/sym10090398

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

1
Faculty of Sciences, Department of Mathematics, Bartın University, Bartın 74100, Turkey
2
Faculty of Sciences, Department of Mathematics, Şeyh Edebali University (Emeritus), Bilecik 11230, Turkey
3
Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea
*
Author to whom correspondence should be addressed.
Received: 21 August 2018 / Revised: 4 September 2018 / Accepted: 10 September 2018 / Published: 12 September 2018
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Abstract

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 in E 4 . We also draw some figures of the rotational hypersurface. View Full-Text
Keywords: four-space; rotational hypersurface; Gauss map; Gaussian curvature; mean curvature; the third Laplace–Beltrami operator four-space; rotational hypersurface; Gauss map; Gaussian curvature; mean curvature; the third Laplace–Beltrami operator
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Güler, E.; Hacısalihoğlu, H.H.; Kim, Y.H. The Gauss Map and the Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space. Symmetry 2018, 10, 398.

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