空间形式中具有径向平均曲率的超曲面

NEXUS Mathematicæ Pub Date : 2021-12-23 DOI:10.5216/nm.v4.70251

Carlos M. C. Riveros, A. M. Vasquez Corro, Edwin O. Salinas Reyes

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引用次数: 0

摘要

本文研究了空间形式Mn+1(c)， c= - 1,0,1中的两类超曲面，即drmc -超曲面和hdrmc -超曲面，这两类超曲面包括|0|中得到的球面型Weingarten超曲面。对于n= 2，我们提出了一种利用两个全纯函数获得M3(c)中的DRMC-surfaces和HDRMC-surfaces的方法。此外，我们还对Mn+1(c)中的drmc -旋转超曲面和Rn+1中的hdrmc -旋转超曲面进行了分类。

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Hypersurfaces with radial mean curvature in space forms

In this paper, we study two classes of hypersurfaces, namely, the DRMC-hypersurfaces and the HDRMC-hypersurfaces in space forms Mn+1(c), c=−1,0,1, these classes include the Weingarten hypersurfaces of the spherical type obtained in |10|. For n= 2, we present a way to obtain DRMC-surfaces and HDRMC-surfaces in M3(c) using two holomorphic functions. Also, we classify the DRMC-hypersurfaces of rotation in Mn+1(c) and the HDRMC-hypersurfaces of rotation in Rn+1.

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NEXUS Mathematicæ

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