Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional

Details Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional

2006-09-12

arxiv.org/abs/math/0609325v2

Siberian Math. J. 48:3 (2007), 395-407

Mathematics

Differential Geometry

21 pages, some typos and references corrected

Scientific paper

We study the generalization of the Willmore functional for surfaces in the three-Heisenberg group. Its construction is based on the spectral theory of the Dirac operator coming to the Weierstrass representation of surfaces (see math.DG/0503707). By using surfaces of revolution we demonstrate that it resembles the Willmore functional for surfaces in the Euclidean space in many geometrical respects. We also observe the relation of these functionals to the isoperimetric problem.

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