Open AccessHarmonic Morphisms Projecting Harmonic Functions to Harmonic Functions
Author(s) -
M. T. Mustafa
Publication year - 2012
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2012/315757
Subject(s) - algorithm , artificial intelligence , computer science
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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