Atsushi Fujioka
Junichi Inoguchi

On some generalisations of constant mean curvature surfaces

(Lobachevskii Journal of Mathematics, Volume III)

In this paper we shall study relations between three generalisations of CMC surfaces- Bonnet surfaces, H-surfaces and HIMC surfaces. We introduce the notion of HIMC surfaces in space forms and show that HIMC surfaces have similar properties to CMC surfaces. Furthermore we shall introduce a special one-parameter family of framings for H- surfaces in the space forms. Through these framings we reveal relationship between the associated family of H-surfaces and the extended solutions for harmonic maps into SO(3).
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