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arXiv · 1211.4826

Darboux transforms of a harmonic inverse mean curvature surface

Katsuhiro Moriya
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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.

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Katsuhiro Moriya. 2012-12-17. Darboux transforms of a harmonic inverse mean curvature surface. https://doi.org/10.1155/2013%2F902092

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