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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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201007098 |
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| _version_ | 1850159883215699968 |
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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). |
| format | Article |
| id | doaj-art-b9864f20e66a42109f813a8a56584cf7 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| 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 |