International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 327-339
Spectral geometry of harmonic maps into warped product manifolds II
Department of Mathematics, Myong Ji University, Kyunggi, Yongin 449-728, Korea
Received 15 March 2001
Copyright © 2001 Gabjin Yun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a closed Riemannian manifold and a warped product manifold of two space forms. We investigate geometric
properties by the spectra of the Jacobi operator of a harmonic map . In particular, we show if is a warped product manifold of Euclidean space with a space form and
are two projectively harmonic maps, then the energy of and are equal up to constant if and are isospectral. Besides, we recover and improve
some results by Kang, Ki, and Pak (1997) and Urakawa (1989).