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Free elasticae and Willmore tori in warped product spaces

Published online by Cambridge University Press:  18 May 2009

Manuel Barros
Manuel Barros
Affiliation:
Departamento De Geometría Y Topología, Facultad De Ciencias, Universidad De Granada, 18071, Granada, Spain Email: Mbarros@goliat.ugr.es
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Abstract

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We 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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 2 , May 1998 , pp. 265 - 272
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

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