Spectral geometry of harmonic maps into warped product manifolds II

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...

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Main Author: Gabjin Yun
Format: Article
Language:English
Published: Wiley 2001-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171201007098
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author Gabjin Yun
author_facet Gabjin Yun
author_sort Gabjin Yun
collection DOAJ
description 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).
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spelling doaj-art-b9864f20e66a42109f813a8a56584cf72025-08-20T02:23:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127632733910.1155/S0161171201007098Spectral geometry of harmonic maps into warped product manifolds IIGabjin Yun0Department of Mathematics, Myong Ji University, Kyunggi, Yongin 449-728, KoreaLet (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).http://dx.doi.org/10.1155/S0161171201007098
spellingShingle Gabjin Yun
Spectral geometry of harmonic maps into warped product manifolds II
International Journal of Mathematics and Mathematical Sciences
title Spectral geometry of harmonic maps into warped product manifolds II
title_full Spectral geometry of harmonic maps into warped product manifolds II
title_fullStr Spectral geometry of harmonic maps into warped product manifolds II
title_full_unstemmed Spectral geometry of harmonic maps into warped product manifolds II
title_short Spectral geometry of harmonic maps into warped product manifolds II
title_sort spectral geometry of harmonic maps into warped product manifolds ii
url http://dx.doi.org/10.1155/S0161171201007098
work_keys_str_mv AT gabjinyun spectralgeometryofharmonicmapsintowarpedproductmanifoldsii