International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 327-339
doi:10.1155/S0161171201007098

Spectral geometry of harmonic maps into warped product manifolds. II

Abstract

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:M→N. In particular, we show if N is a warped product manifold of Euclidean space with a space form and ϕ,ψ:M→N 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).