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

Rafael López, Álvaro Pámpano

Type: Article

Publication Date: 2020-02-06

Citations: 24

DOI: https://doi.org/10.1002/mana.201800235

Abstract

Abstract We classify all rotational surfaces in Euclidean space whose principal curvatures κ 1 and κ 2 satisfy the linear relation , 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.

Locations

arXiv (Cornell University) - View - PDF
Mathematische Nachrichten - View

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