Tatsuyoshi Hamada,Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-0180, Japan; e-mail: hamada@fukuoka-u.ac.jp

Katsufumi Yamashita,Department of Mathematics, Saga University, Saga, 840-8502, Japan; e-mail: ky-karatsucity@sgr.bbiq.jp

Abstract/Résumé:

In Theorem 1, we show a new condition for a real hypersurface \(M\) isometrically immersed into a nonflat complex space form to be a hypersurface of type (A). This condition is expressed by the parallelism of a certain tensor of type (1, 1) on \(M\) . Furthermore, using the discussion in the proof of Theorem 1, we can give a condition for a Kähler manifold to be a complex space form (see Theorem 2).

Dans le théorème 1, nous donnons une nouvelle condition pour qu’une hypersurface réelle \(M\) immergée dans une “space form” complexe non plate soit une hypersurface de type (A). Cette condition est exprimée par le parallélisme d’un certain tenseur de type (1, 1) sur \(M\) . De plus, en utilisant la discussion dans la démonstration du théorème 1, nous donnons une condition pour qu’une variété de Kähler soit une “space form” complexe (voir le théorème 2).

Keywords: Kahler manifold, complex space form, real hypersurfaces of type (A), structure tensor

AMS Subject Classification: Local submanifolds, Geodesics, Global submanifolds 53B25, 53C22, 53C40

PDF(click to download): The Parallelism of a Certain Tensor of Real Hypersurfaces in a Nonflat Complex Space Form

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

PDF(click to download): Nonnegatively Curved Geodesic Spheres in a Complex Hyperbolic Space

Sadahiro Maeda, Department of Mathematics, Shimane University, Matsue 690-8504, Japan; email: smaeda@riko.shimane-u.ac.jp

Abstract/Résumé:

Investigating geometric properties of characteristic vector fields on geodesic spheres in a complex space form, we characterize complex space forms in the class of Kähler manifolds.

En étudiant des propriétés géométriques de champs de vecteurs caractéristiques sur des sphères géodésiques dans un espace complexe à courbure constante, on caractérise ces espaces dans la classe des variétés kähleriennes.

Keywords: Geodesic spheres, Kahler manifolds, Killing vector fields, characteristic fields, complex space forms, totally geodesic complex curves

AMS Subject Classification: Local submanifolds 53B25

PDF(click to download): Characterization of complex space forms in terms of characteristic vector fields on geodesic spheres

T. Adachi / S. Ma

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Naturally reductive Riemannian homogeneous manifolds, geodesies, hypersurfaces of type (A), nonflat complex space forms, normal curvature, real hypersurfaces, structure torsion

AMS Subject Classification: Local submanifolds 53B25

PDF(click to download): A Congruence Theorem of Geodesies on Some Naturally Reductive Riemannian Homogeneous Manifolds

K. Suizu / S. Maeda / T. Adachi

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Veronese imbeddings, circle, complex projective space

AMS Subject Classification: Local submanifolds 53B25

PDF(click to download): A characterization of Veronese imbeddings into complex projective spaces by circles