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CHARACTERISATIONS OF GEODESIC HYPERSPHERES IN A NON-FLAT COMPLEX SPACE FORM

Published online by Cambridge University Press:  02 August 2012

SADAHIRO MAEDA,
TOSHIAKI ADACHI and
YOUNG HO KIM
SADAHIRO MAEDA
Affiliation:
Department of Mathematics, Saga University, Saga 840-8502, Japan e-mail: smaeda@ms.saga-u.ac.jp
TOSHIAKI ADACHI
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Nagoya 466-8555, Japan e-mail: adachi@nitech.ac.jp
YOUNG HO KIM
Affiliation:
Department of Mathematics, Teachers College, Kyungpook National University, Taegu 702-701, Korea e-mail: yhkim@knu.ac.kr
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Abstract

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Totally η-umbilic real hypersurfaces are the simplest examples of real hypersurfaces in a non-flat complex space form. Geodesic hyperspheres in this ambient space are typical examples of such real hypersurfaces. We characterise every geodesic hypersphere by observing the extrinsic shapes of its geodesics and using the derivative of its contact form.

Keywords

Primary 53B25Secondary 53C40

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013, pp. 217 - 227
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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