Glasgow Mathematical Journal

Table of Contents - 2003 - Volume 45, Issue 01  


REAL HYPERSURFACES IN QUATERNIONIC PROJECTIVE SPACES WITH COMMUTING TANGENT JACOBI OPERATORS

MIGUEL ORTEGA a1, JUAN DE DIOS PÉREZ a1 and YOUNG JIN SUH a2
a1 Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain e-mail: miortega@ugr.es, jdperez@ugr.es
a2 Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea e-mail: yjsuh@kyungpook.ac.kr

Abstract

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.

(Received June 13 2001)
(Accepted March 22 2002)

Maths Classification

53C15; 53B25.