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Biminimal immersions

E. Loubeau·S. Montaldo
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Abstract

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 to biminimal immersions for: i) biminimal curves in a Riemannian manifold, with particular care to the case of curves in a space form ii) isometric immersions of codimension one in a Riemannian manifold, in particular for surfaces of a three-dimensional manifold. We describe two methods to construct families of biminimal surfaces using both Riemannian and horizontally homothetic submersions.

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E. Loubeau, S. Montaldo. 2007-01-08. Biminimal immersions. https://arxiv.org/abs/math/0405320

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