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arXiv · 1303.6391

Noether invariants for constant mean curvature surfaces in 3-dimensional homogeneous spaces

Sébastien Cartier
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Abstract

We give explicit formul{\ae} for Noether invariants associated to Killing vector fields for the variational problem of minimal and constant mean curvature surfaces in 3-manifolds. In the case of homogeneous spaces, such invariants are the flux (associated to translations) and the torque (associated to rotations). Then we focus on homogeneous spaces with isometry groups of dimensions 3 or 4 and study the behavior of these invariants under the action of isometries. Finally, we give examples of actual computations and of interpretations of these invariants in different situations.

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Sébastien Cartier. 2013-03-26. Noether invariants for constant mean curvature surfaces in 3-dimensional homogeneous spaces. https://arxiv.org/abs/1303.6391

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