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).