## Abstract and Applied Analysis

### Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

M. T. Mustafa

#### Abstract

For Riemannian manifolds $M$ and $N$, admitting a submersion $\varphi$ 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 $U={\varphi }^{-1}(V)\subset M$ projects down, via its horizontal component, to a harmonic function on $V\subset N$.

#### 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

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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