On Closed Weingarten Surfaces

• Autores: Wolfgang Kühnel, Michael Steller
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 146, Nº 2, 2005, págs. 113-126
• Idioma: inglés
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• Resumen

  • We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations ? = F(?) between the principal curvatures ?, ?. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(?) = c?2n+1. This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(?) = c?3.