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2012 Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions
M. T. Mustafa
Abstr. Appl. Anal. 2012(SI13): 1-8 (2012). DOI: 10.1155/2012/315757


For Riemannian manifolds M and N, admitting a submersion ϕ with compact fibres, we introduce the projection of a function via its decomposition intohorizontal and vertical components. By comparing the Laplacians on M and N, we determine conditions under which a harmonic function on U=ϕ1(V)M projects down, via its horizontal component, to a harmonic function on VN.


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M. T. Mustafa. "Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions." Abstr. Appl. Anal. 2012 (SI13) 1 - 8, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1245.53053
MathSciNet: MR2926889
Digital Object Identifier: 10.1155/2012/315757

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI13 • 2012
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