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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… Click to show full 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.
Keywords:
linear relation;
principal curvatures;
euclidean space;
surfaces euclidean;
rotational surfaces
Journal Title: Mathematische Nachrichten
Year Published: 2020
Link to full text (if available)
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Journal Title: Mathematische Nachrichten
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!