Monatshefte für Mathematik

, Volume 146, Issue 2, pp 113–126

On Closed Weingarten Surfaces

  • Wolfgang Kühnel
  • Michael Steller

DOI: 10.1007/s00605-005-0313-4

Cite this article as:
Kühnel, W. & Steller, M. Mh Math (2005) 146: 113. doi:10.1007/s00605-005-0313-4


We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations κ = F(λ) between the principal curvatures κ, λ. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(λ) = cλ2n+1. This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(λ) = cλ3.

2000 Mathematics Subject Classifications: 53A05, 53C40
Key words: Curvature diagram, surface of revolution, Hopf surface, Weingarten surface

Copyright information

© Springer-Verlag/Wien 2005

Authors and Affiliations

  • Wolfgang Kühnel
    • 1
  • Michael Steller
    • 1
  1. 1.Universität StuttgartGermany