Darboux Transforms of a Harmonic Inverse Mean Curvature Surface. (7th April 2013)

• Record Type: Journal Article
• Authors: Moriya, Katsuhiro
• Other Names: Sanchis Manuel Academic Editor.
• Is Part Of: Geometry. Volume 2013(2013)
• Publication Date: 2013-04-07
• Subjects: Geometry -- Periodicals; Geometry; Periodicals; 516
• DOI: 10.1155/2013/902092
• Languages: English
• ISSNs: 2314-422X

Abstract

Abstract : The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund 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 Bäcklund 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 Painlevé III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution.