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On Closed Weingarten Surfaces

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Abstract.

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.

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Authors and Affiliations

  1. Universität Stuttgart, Germany

    Wolfgang Kühnel & Michael Steller

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  1. Wolfgang Kühnel
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  2. Michael Steller
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Kühnel, W., Steller, M. On Closed Weingarten Surfaces. Mh Math 146, 113–126 (2005). https://doi.org/10.1007/s00605-005-0313-4

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  • DOI: https://doi.org/10.1007/s00605-005-0313-4

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