Tokyo Journal of Mathematics

$S^{1}$-equivariant CMC-hypersurfaces in the Hyperbolic 3-space and the Corresponding Lagrangians

Keiichi KIKUCHI

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Abstract

A family of $S^{1}$-equivariant hypersurfaces of constant mean curvature can be obtained by using the Lagrangians with suitable potentials in the hyperbolic 3-space. The conservation law is effectively applied to the construction of $S^{1}$-equivariant hypersurfaces of constant mean curvature in the hyperbolic 3-space.

Article information

Source
Tokyo J. Math., Volume 36, Number 1 (2013), 207-213.

Dates
First available in Project Euclid: 22 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1374497520

Digital Object Identifier
doi:10.3836/tjm/1374497520

Mathematical Reviews number (MathSciNet)
MR2976548

Zentralblatt MATH identifier
1277.53054

Subjects
Primary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]
Secondary: 70H05: Hamilton's equations 70H33: Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction

Citation

KIKUCHI, Keiichi. $S^{1}$-equivariant CMC-hypersurfaces in the Hyperbolic 3-space and the Corresponding Lagrangians. Tokyo J. Math. 36 (2013), no. 1, 207--213. doi:10.3836/tjm/1374497520. https://projecteuclid.org/euclid.tjm/1374497520


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