Gauss map harmonicity and mean curvature of a hypersurface in a homogeneous manifold

• Autores: Fidelis Bittencourt, Jaime B. Ripoll
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 224, Nº 1, 2006, págs. 45-64
• Idioma: inglés
• DOI: 10.2140/pjm.2006.224.45
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• Resumen

  • We define a Gauss map of an orientable hypersurface in a homogeneous manifold with an invariant Riemannian metric. Our main objective is to extend to this setting some results on the Gauss map of a constant mean curvature hypersurface of an Euclidean space, namely the Ruh¿Vilm theorem relating the harmonicity of the Gauss map and the constancy of the mean curvature, and the Hoffman¿Osserman¿Schoen theorem characterizing the plane and the circular cylinder as the only complete constant mean curvature surfaces whose Gauss image is contained in a closed hemisphere of the sphere.