Abstract and Applied Analysis

Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

M. T. Mustafa

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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 = ϕ 1 ( V ) M projects down, via its horizontal component, to a harmonic function on V N .

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Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 315757, 8 pages.

First available in Project Euclid: 5 April 2013

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Mustafa, M. T. Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 315757, 8 pages. doi:10.1155/2012/315757. https://projecteuclid.org/euclid.aaa/1365168179

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