SO(2)-invariant minimal and constant mean curvature surfaces. (English) Zbl 0827.53009

The authors endow \(\mathbb{R}^3\) with a certain classical 2-parameter family of homogeneous metrics whose isometry groups have dimension or 6, and then examine invariant constant mean curvature surfaces in these. Then description is made via an ODE which admits a prime integral.


53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
Full Text: DOI EuDML


[1] [Be]M. Bekkar,Exemples de surfaces minimales dans l’espace de Heisenberg, Rend. Sem. Fac. Sci. M.F.N. Cagliari, vol. 61, 2, (1991) pp. 123–130 · Zbl 0792.53056
[2] [BS]M. Bekkar andT. Sari,Surfaces minimales reglées dans l’espace de Heisenberg H 3, Rend. Sem. Mat. Univ. e Politec. Torino, vol. 50, 3, (1992) pp. 243–254 · Zbl 0810.53012
[3] [Bi]L. Bianchi,Lezioni sulla teoria dei gruppi continui e finiti di transformazioni, Ed. Zanichelli, Bologna (1928) · JFM 54.0442.01
[4] [Ca]É. Cartan,Leçons sur la géométrie des espaces de Riemann, Gauthier Villars, Paris (1946)
[5] [ER]J. Eells andA. Ratto,Harmonic maps and minimal immersions with symmetries, Annals of Mathematics Studies, Princeton University Press 130, (1993) pp. 1–228 · Zbl 0783.58003
[6] [Hs]W.Y. Hsiang,Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces I, J. Diff. Geom. 17 (1982), pp. 337–356 · Zbl 0493.53043
[7] [Pi]P. Piu,Sur certains types de distributions non-integrables totalement géodésiques, Thèse de Doctorat, Univ. de Haute Alsace, (1988)
[8] [Vr]G. Vranceanu,Leçons de géométrie différentielle, Ed. Acad. Rep. Pop. Roum., vol I, Bucarest (1957)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.