English

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

Differential Geometry 2007-05-23 v3

Abstract

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.

Keywords

Cite

@article{arxiv.math/0504124,
  title  = {Surfaces and fronts with harmonic-mean curvature one in hyperbolic three-space},
  author = {Masatoshi Kokubu},
  journal= {arXiv preprint arXiv:math/0504124},
  year   = {2007}
}

Comments

20 pages, 9 figures; Section 3 revised

R2 v1 2026-07-22T17:17:49.352Z