Abstract and Applied Analysis

Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

M. T. Mustafa

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Abstract

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 .

Article information

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

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168179

Digital Object Identifier
doi:10.1155/2012/315757

Mathematical Reviews number (MathSciNet)
MR2926889

Zentralblatt MATH identifier
1245.53053

Citation

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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