Advanced Studies in Pure Mathematics

Cyclic Hypersurfaces of Constant Curvature

Rafael López

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Abstract

We study hypersurfaces in Euclidean, hyperbolic or Lorentz-Minkowski space with the property that it is foliated by a one-parameter family of round spheres. We describe partially such hypersurfaces with some assumption on its curvature. In general, we shall consider the situation that the mean curvature or the Gaussian curvature is constant.

Article information

Source
Minimal Surfaces, Geometric Analysis and Symplectic Geometry, K. Fukaya, S. Nishikawa and J. Spruck, eds. (Tokyo: Mathematical Society of Japan, 2002), 185-199

Dates
First available in Project Euclid: 31 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546230297

Digital Object Identifier
doi:10.2969/aspm/03410185

Mathematical Reviews number (MathSciNet)
MR1925739

Zentralblatt MATH identifier
1026.53034

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

López, Rafael. Cyclic Hypersurfaces of Constant Curvature. Minimal Surfaces, Geometric Analysis and Symplectic Geometry, 185--199, Mathematical Society of Japan, Tokyo, Japan, 2002. doi:10.2969/aspm/03410185. https://projecteuclid.org/euclid.aspm/1546230297


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