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

Gabjin Yun

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 (Mn,g) be a closed Riemannian manifold and N a warped product manifold of two space forms. We investigate geometric properties by the spectra of the Jacobi operator of a harmonic map ϕ:MN. In particular, we show if N is a warped product manifold of Euclidean space with a space form and ϕ,ψ:MN are two projectively harmonic maps, then the energy of ϕ and ψ are equal up to constant if ϕ and ψ are isospectral. Besides, we recover and improve some results by Kang, Ki, and Pak (1997) and Urakawa (1989).