Taiwanese Journal of Mathematics

ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE WITH CONSTANT MEAN CURVATURE

Ugur Dursun

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Abstract

We give explicit parameterizations of rotation hypersurfaces in Lorentz-Minkowski space $L^{n+1}$. Then we obtain rotation hypersurfaces in Lorentz-Minkowski space $L^{n+1}$ with constant mean curvature. In particular, we determine nonplanar rotation hypersurfaces with zero mean curvature, namely, generalized catenoids of $L^{n+1}$. In the case the rotation axis is light-like, the generalized catenoids generalize Enneper's surfaces of the 2nd and 3rd kind.

Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 685-705.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405814

Digital Object Identifier
doi:10.11650/twjm/1500405814

Mathematical Reviews number (MathSciNet)
MR2655794

Zentralblatt MATH identifier
1206.53066

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
rotation hypersurface constant mean curvature catenoid Enneper's hypersurface

Citation

Dursun, Ugur. ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE WITH CONSTANT MEAN CURVATURE. Taiwanese J. Math. 14 (2010), no. 2, 685--705. doi:10.11650/twjm/1500405814. https://projecteuclid.org/euclid.twjm/1500405814


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