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

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• 作者：D. A. Berdinsky and I. A. Taimanov
• 关键词：Heisenberg group ; surface of revolution ; isoperimetric problem ; Willmore functional
• 刊名：Siberian Mathematical Journal
• 出版年：2007
• 出版时间：May, 2007
• 年：2007
• 卷：48
• 期：3
• 页码：395-407
• 全文大小：203 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9260

文摘

We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem.