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J. Korean Math. Soc. 1997; 34(2): 483-500

Printed June 1, 1997

Copyright © The Korean Mathematical Society.

On the spectral geometry for the Jacobi operators of harmonic maps into product manifolds

Tae Ho Kang, U-Hang Ki, and Jin Suk Pak

University of Ulsan, Kyungpook National University and Kyungpook National University

Abstract

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We investigate the geometric properties reflected by the spectra of the Jacobi operator of a harmonic map when the target manifold is a Riemannian product manifold or a Kaehlerian product manifold. And also we study the spectral characterization of Riemannian sumersions when the target manifold is $S^n\times S^n$ or $CP^n \times CP^n$.

Keywords: Spectral geometry, Jacobi operators, harmonic maps, Kaehlerian product manifolds, harmonic morphisms

MSC numbers: 58G25

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