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Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator

Published:2008-09-01
Printed: Sep 2008
• Jong Taek Cho
• U-Hang Ki
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Abstract

Real hypersurfaces in a complex space form whose structure Jacobi operator is symmetric along the Reeb flow are studied. Among them, homogeneous real hypersurfaces of type $(A)$ in a complex projective or hyperbolic space are characterized as those whose structure Jacobi operator commutes with the shape operator.
 Keywords: complex space form, real hypersurface, structure Jacobi operator
 MSC Classifications: 53B20 - Local Riemannian geometry 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)

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