Surfaces and fronts with harmonic-mean curvature one in hyperbolic three-space

Details Surfaces and fronts with harmonic-mean curvature one in hyperbolic three-space Surfaces and fronts with harmonic-mean curvature one in hyperbolic three-space

2005-04-07

arxiv.org/abs/math/0504124v3

Mathematics

Differential Geometry

20 pages, 9 figures; Section 3 revised

Scientific paper

We investigate surfaces with constant harmonic-mean curvature one (HMC-1 surfaces) in hyperbolic three-space. We allow them to have certain kinds of singularities, and discuss some global properties. As well as flat surfaces and surfaces with constant mean curvature one (CMC-1 surfaces), HMC-1 surfaces belong to a certain class of Weingarten surfaces. From the viewpoint of parallel surfaces, CMC-1 surfaces and HMC-1 surfaces are representative among this class.

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