About: Harmonic morphism

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In mathematics, a harmonic morphism is a (smooth) map between Riemannian manifolds that pulls back real-valued harmonic functions on the codomain to harmonic functions on the domain. Harmonic morphisms form a special class of harmonic maps i.e. those that are horizontally (weakly) conformal. In local coordinates, on and on , the harmonicity of is expressed by the non-linear system where and are the Christoffel symbols on and , respectively. The horizontal conformality is given by

Property Value
dbo:abstract
  • In mathematics, a harmonic morphism is a (smooth) map between Riemannian manifolds that pulls back real-valued harmonic functions on the codomain to harmonic functions on the domain. Harmonic morphisms form a special class of harmonic maps i.e. those that are horizontally (weakly) conformal. In local coordinates, on and on , the harmonicity of is expressed by the non-linear system where and are the Christoffel symbols on and , respectively. The horizontal conformality is given by where the conformal factor is a continuous function called the dilation. Harmonic morphisms are therefore solutions to non-linear over-determined systems of partial differential equations, determined by the geometric data of the manifolds involved. For this reason, they are difficult to find and have no general existence theory, not even locally. (en)
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 45283151 (xsd:integer)
dbo:wikiPageLength
  • 4995 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1054381547 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdfs:comment
  • In mathematics, a harmonic morphism is a (smooth) map between Riemannian manifolds that pulls back real-valued harmonic functions on the codomain to harmonic functions on the domain. Harmonic morphisms form a special class of harmonic maps i.e. those that are horizontally (weakly) conformal. In local coordinates, on and on , the harmonicity of is expressed by the non-linear system where and are the Christoffel symbols on and , respectively. The horizontal conformality is given by (en)
rdfs:label
  • Harmonic morphism (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License