Experimental Mathematics

Constant-Mean-Curvature Surfaces with Singularities in Minkowski 3-Space

Yuhei Umeda

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Abstract

We shall investigate spacelike constant-mean-curvature surfaces with singularities in Minkowski 3-space. Recently, Kokubu, Rossman, Saji, Umehara, and Yamada gave useful criteria for cuspidal edges and swallowtails. Applying their criteria, we define a new class of generalized constant-mean-curvature surface and give some examples with cuspidal edges and swallowtails.

Article information

Source
Experiment. Math., Volume 18, Issue 3 (2009), 311-323.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.em/1259158468

Mathematical Reviews number (MathSciNet)
MR2555701

Zentralblatt MATH identifier
1182.53008

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20] 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
CMC surface Gauss map cuspidal edge swallowtail singularity

Citation

Umeda, Yuhei. Constant-Mean-Curvature Surfaces with Singularities in Minkowski 3-Space. Experiment. Math. 18 (2009), no. 3, 311--323. https://projecteuclid.org/euclid.em/1259158468


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