Classification of rotational surfaces in Euclidean space satisfying a linear relation between their principal curvatures
Copyright policy )Classification of rotational surfaces in Euclidean space satisfying a linear relation between their principal curvatures
AbstractWe classify all rotational surfaces in Euclidean space whose principal curvatures κ1 and κ2 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.
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), rotational surface, Mathematics - Differential Geometry, Curves in Euclidean and related spaces, 53A10, 53C42, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, principal curvature, Weingarten surface, Surfaces in Euclidean and related spaces, phase plane, Differential Geometry (math.DG), FOS: Mathematics
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), rotational surface, Mathematics - Differential Geometry, Curves in Euclidean and related spaces, 53A10, 53C42, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, principal curvature, Weingarten surface, Surfaces in Euclidean and related spaces, phase plane, Differential Geometry (math.DG), FOS: Mathematics
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