Free elasticae and Willmore tori in warped product spaces-Reference-Cited by-同舟云学术

Free elasticae and Willmore tori in warped product spaces

Published:1998-05 Issue:2 Volume:40 Page:265-272
ISSN:0017-0895
Container-title:Glasgow Mathematical Journal
language:en
Short-container-title:Glasgow Math. J.

Author:

Barros Manuel

Abstract

AbstractWe use the principle of symmetric criticality to connect the Willmore variational problem for surfaces in a warped product space with base a circle, and the free elastica variational problem for curves on its fiber. In addition we obtain a rational oneparameter family of closed helices in the anti De Sitter 3-space which are critical points of the total squared curvature functional. This means they are free elasticae. Also they are spacelike; this allows us to construct a corresponding family of spacelike Willmore tori in a certain kind of spacetime close to the Robertson-Walker spaces.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference15 articles.

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3. 6. Barros M. and Garay O. J. , Hopf submanifolds in S 7 which are Willmore-Chen submanifolds, Math. Z., to appear.

4. Stationary 2-type surfaces in a hypersphere

5. 5. Barros M. , Ferrandez A. , Lucas P. and Meroño M. A. , Willmore tori into pseudo-Riemannian space forms of low dimension, preprint (1996).

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