Harmonicity of horizontally conformal maps and spectrum of the Laplacian
We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if Φ:M→N is a horizontally conformal map such that the tension field is divergence free, then Φ is harmonic. Furthermore, if N is noncompact, then Φ must be constant. Also...
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| Language: | English |
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202107058 |
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doaj-f6439bd46865456c8066ff89ecebfc232020-11-24T21:17:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01301270971510.1155/S0161171202107058Harmonicity of horizontally conformal maps and spectrum of the LaplacianGabjin Yun0Department of Mathematics, Myong Ji University, San 38-2, Namdong, Yongin, Kyunggi 449-728, KoreaWe discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if Φ:M→N is a horizontally conformal map such that the tension field is divergence free, then Φ is harmonic. Furthermore, if N is noncompact, then Φ must be constant. Also we show that the projection of a warped product manifold onto the first component is harmonic if and only if the warping function is constant. Finally, we describe a characterization for a horizontally conformal map with a constant dilation preserving an eigenfunction.http://dx.doi.org/10.1155/S0161171202107058 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Gabjin Yun |
| spellingShingle |
Gabjin Yun Harmonicity of horizontally conformal maps and spectrum of the Laplacian International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Gabjin Yun |
| author_sort |
Gabjin Yun |
| title |
Harmonicity of horizontally conformal maps and spectrum of the Laplacian |
| title_short |
Harmonicity of horizontally conformal maps and spectrum of the Laplacian |
| title_full |
Harmonicity of horizontally conformal maps and spectrum of the Laplacian |
| title_fullStr |
Harmonicity of horizontally conformal maps and spectrum of the Laplacian |
| title_full_unstemmed |
Harmonicity of horizontally conformal maps and spectrum of the Laplacian |
| title_sort |
harmonicity of horizontally conformal maps and spectrum of the laplacian |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
We discuss the harmonicity of horizontally conformal maps and
their relations with the spectrum of the Laplacian. We prove that if Φ:M→N is a horizontally conformal map such that the tension field is divergence free, then Φ is harmonic. Furthermore, if N is noncompact, then Φ must be constant. Also we show that the projection of a warped product manifold onto the first component is harmonic if and only if the warping function is constant. Finally, we describe a characterization for a horizontally conformal map with a constant dilation preserving an eigenfunction. |
| url |
http://dx.doi.org/10.1155/S0161171202107058 |
| work_keys_str_mv |
AT gabjinyun harmonicityofhorizontallyconformalmapsandspectrumofthelaplacian |
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