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arXiv:math/0609325 [math.DG]AbstractReferencesReviewsResources

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

Dmitry A. Berdinsky, Iskander A. Taimanov

Published 2006-09-12, updated 2006-10-19Version 2

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.

Comments: 21 pages, some typos and references corrected
Journal: Siberian Math. J. 48:3 (2007), 395-407
Categories: math.DG
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