Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions
For Riemannian manifolds M and N, admitting a submersion ϕ with compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians on M and N, we determine conditions under which a harmonic function on U=ϕ−1(V)⊂M proje...
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Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2012-01-01
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Series: | Abstract and Applied Analysis |
Online Access: | http://dx.doi.org/10.1155/2012/315757 |