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BIMINIMAL IMMERSIONS

Published online by Cambridge University Press:  28 July 2008

E. Loubeau  and
S. Montaldo
E. Loubeau
Affiliation:
Département de Mathématiques, Université de Bretagne, Occidentale 6, avenue Victor Le Gorgeu CS 93837, 29238 Brest Cedex 3, France ([email protected])
S. Montaldo
Affiliation:
Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy ([email protected])
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Abstract

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We study biminimal immersions: that is, immersions which are critical points of the bienergy for normal variations with fixed energy. We give a geometrical description of the Euler–Lagrange equation associated with biminimal immersions for both biminimal curves in a Riemannian manifold, with particular attention given to the case of curves in a space form, and isometric immersions of codimension 1 in a Riemannian manifold, in particular for surfaces of a three-dimensional manifold. We describe two methods of constructing families of biminimal surfaces using both Riemannian and horizontally homothetic submersions.

Keywords

Primary 58E20biminimal surfacesbiharmonic mapsWillmore functionalThurston geometry
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 2 , June 2008 , pp. 421 - 437
Copyright
Copyright © Edinburgh Mathematical Society 2008