TOTALLY η-UMBILIC HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM AND THEIR ALMOST CONTACT METRIC STRUCTURES

BYUNG HAK KIM; SADAHIRO MAEDA

doi:10.32219/isms.72.3_289

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Keywords: real hypersurfaces, nonflat complex space forms, totally η-umbilc hypersurfaces, geodesics, circles, contact manifolds, Sasakian manifolds, Sasakian space forms, K-contact manifolds, nearly Sasakian manifolds

JOURNAL FREE ACCESS

2010 Volume 72 Issue 3 Pages 289-296

DOI https://doi.org/10.32219/isms.72.3_289

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Abstract

We bridge between submanifold theory and contact geometry. We give a geometric meaning of some fundamental notions such as Sasakian, nearly Sasakian, Kcontact from the viewpoint of the result in [3] (Theorem 1). Moreover, motivated by the notion of totally η-umbilic hypersurfaces in a nonflat complex space form, we give a new notion in contact geometry (Theorem 2).

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