Darboux transforms of a harmonic inverse mean curvature surface
Differential Geometry
2013-04-11 v2 Classical Analysis and ODEs
Abstract
The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward B\"{a}cklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward B\"{a}cklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlev\'{e} III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution.
Keywords
Cite
@article{arxiv.1211.4826,
title = {Darboux transforms of a harmonic inverse mean curvature surface},
author = {Katsuhiro Moriya},
journal= {arXiv preprint arXiv:1211.4826},
year = {2013}
}
Comments
16 pages, major revision