Biminimal immersions

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.

Dedicated to Professor Renzo Caddeo on his 60th birthday. 2 figures

Cited by in corpus (8)

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• Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries
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• On the Existence of Closed Biconservative Surfaces in Space Forms
• Reduction methods for the bienergy
• f-Biharmonic and bi-f-harmonic submanifolds of generalized space forms
• Proper Biconservative immersions into the Euclidean space
• Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor