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Pré-Publication, Document De Travail Année : 2013

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

Résumé

We give explicit formulæ 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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Dates et versions

hal-00804612 , version 1 (25-03-2013)

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Sébastien Cartier. Noether invariants for constant mean curvature surfaces in 3-dimensional homogeneous spaces. 2013. ⟨hal-00804612⟩
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