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- Title
Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions.
- Authors
Mustafa, M. T.
- Abstract
For Riemannian manifolds M and N, admitting a submersion φ with compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians on M and N, we determine conditions under which a harmonic function on U = φ-1 (V) C M projects down, via its horizontal component, to a harmonic function on V c N.
- Subjects
HARMONIC morphisms; HARMONIC functions; RIEMANNIAN manifolds; SUBMERSIONS (Mathematics); MATHEMATICAL decomposition; COMPARATIVE studies; LAPLACIAN operator
- Publication
Abstract & Applied Analysis, 2012, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2012/315757