Nonnegatively Curved Geodesic Spheres in a Complex Hyperbolic Space

C. R. Math. Rep. Acad. Sci. Canada Vol. 35 (3) 2013, pp. 114–120

September 30, 2013

Sadahiro Maeda, Department of Mathematics, Saga University, Saga, 840-8502, Japan; e-mail: smaeda@ms.saga- u.ac.jp

Abstract/Résumé:

We characterize geodesic spheres with sufficiently small radii in a complex hyperbolic space by using their geometric properties. These geodesic spheres are the only examples of hypersurfaces of type (A) having nonnegative sectional curvature in this ambient space.

Nous caractérisons les sphères géodésiques de rayon suffisamment petit dans un espace hyperbolique complexe en utilisant leurs propriétés géométriques. Ces sphères géodésiques sont les seuls exemples d’hypersurfaces de type (A) qui ont courbure non-negative dans cet espace ambiant.

Keywords: Geodesic spheres, circles, complex hyperbolic spaces, contact form, exterior differentiation, geodesics, hypersurfaces of type (A), sectional curvatures
AMS Subject Classification: Local submanifolds 53B25

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