Biminimal immersions

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 equa- tion 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 codimen- sion 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.