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REAL HYPERSURFACES IN QUATERNIONIC PROJECTIVE SPACES WITH COMMUTING TANGENT JACOBI OPERATORS

Published online by Cambridge University Press:  01 May 2003

MIGUEL ORTEGA ,
JUAN DE DIOS PÉREZ  and
YOUNG JIN SUH
MIGUEL ORTEGA
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain e-mail: miortega@ugr.es, jdperez@ugr.es
JUAN DE DIOS PÉREZ
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain e-mail: miortega@ugr.es, jdperez@ugr.es
YOUNG JIN SUH
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea e-mail: yjsuh@kyungpook.ac.kr
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Abstract

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From the classical differential equation of Jacobi fields, one naturally defines the Jacobi operator of a Riemannian manifold with respect to any tangent vector. A straightforward computation shows that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute. In this way, we classify the real hypersurfaces in quaternionic projective spaces all of whose tangent Jacobi operators commute.

Keywords

53C1553B25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 79 - 89
Copyright
2003 Glasgow Mathematical Journal Trust