structure tensor — 1 articles found.

The Parallelism of a Certain Tensor of Real Hypersurfaces in a Nonflat Complex Space Form

C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (3) 2015, pp. 81-88
Vol.37 (3) 2015
Tatsuyoshi Hamada; Katsufumi Yamashita Details
(Received: 2014-10-15 , Revised: 2014-11-04 )
(Received: 2014-10-15 , Revised: 2014-11-04 )

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

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