Classification of rotational surfaces in Euclidean space satisfying a linear relation between their principal curvatures

Rafael López and Álvaro Pámpano

Mathematische Nachrichten, 2020, vol. 293, issue 4, 735-753

Abstract: We classify all rotational surfaces in Euclidean space whose principal curvatures κ1 and κ2 satisfy the linear relation κ1=aκ2+b, where a and b are two constants. As a consequence of this classification, we find closed (embedded and not embedded) surfaces and periodic (embedded and not embedded) surfaces with a geometric behaviour similar to Delaunay surfaces. Finally, we give a variational characterization of the generating curves of these surfaces.

Date: 2020
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https://doi.org/10.1002/mana.201800235

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