Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

M. T. Mustafa

Abstract and Applied Analysis, 2012, vol. 2012, 1-8

Abstract:

For Riemannian manifolds and , admitting a submersion with compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians on and , we determine conditions under which a harmonic function on projects down, via its horizontal component, to a harmonic function on .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:315757

DOI: 10.1155/2012/315757

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