About: Geodesic map

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In mathematics—specifically, in differential geometry—a geodesic map (or geodesic mapping or geodesic diffeomorphism) is a function that "preserves geodesics". More precisely, given two (pseudo-)Riemannian manifolds (M, g) and (N, h), a function φ : M → N is said to be a geodesic map if * φ is a diffeomorphism of M onto N; and * the image under φ of any geodesic arc in M is a geodesic arc in N; and * the image under the inverse function φ−1 of any geodesic arc in N is a geodesic arc in M.

Attributes	Values
rdf:type	disease
rdfs:label	Geodesic map (en) Geodetische afbeelding (nl)
rdfs:comment	In mathematics—specifically, in differential geometry—a geodesic map (or geodesic mapping or geodesic diffeomorphism) is a function that "preserves geodesics". More precisely, given two (pseudo-)Riemannian manifolds (M, g) and (N, h), a function φ : M → N is said to be a geodesic map if * φ is a diffeomorphism of M onto N; and * the image under φ of any geodesic arc in M is a geodesic arc in N; and * the image under the inverse function φ−1 of any geodesic arc in N is a geodesic arc in M. (en) In de wiskunde, speciaal in de differentiaalmeetkunde, is een geodetische afbeelding een afbeelding die geodeten behoudt. (nl)
dcterms:subject	Differential geometry Geodesic (mathematics)
Wikipage page ID	13636507 (xsd:integer)
Wikipage revision ID	1117686399 (xsd:integer)
Link from a Wikipage to another Wikipage	Beltrami-Klein model Differential geometry Mathematics Geodesic (mathematics) Function (mathematics) Geodesic Gnomonic projection Euclidean space Diffeomorphism Pseudo-Riemannian manifold Radius Riemannian manifold Riemannian metric Inverse function Isometry Hyperbolic geometry Homeomorphism Differential geometry Dimension Identity function Hypersphere Poincaré disc model Unit disc
sameAs	Geodesic map Geodesic map Geodesic map Geodesic map
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:MathWorld
title	Geodesic mapping (en)
urlname	GeodesicMapping (en)
has abstract	In mathematics—specifically, in differential geometry—a geodesic map (or geodesic mapping or geodesic diffeomorphism) is a function that "preserves geodesics". More precisely, given two (pseudo-)Riemannian manifolds (M, g) and (N, h), a function φ : M → N is said to be a geodesic map if * φ is a diffeomorphism of M onto N; and * the image under φ of any geodesic arc in M is a geodesic arc in N; and * the image under the inverse function φ−1 of any geodesic arc in N is a geodesic arc in M. (en) In de wiskunde, speciaal in de differentiaalmeetkunde, is een geodetische afbeelding een afbeelding die geodeten behoudt. (nl)
gold:hypernym	Function
prov:wasDerivedFrom	wikipedia-en:Geodesic_map?oldid=1117686399&ns=0
page length (characters) of wiki page	3668 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Geodesic_map
is Link from a Wikipage to another Wikipage of	Beltrami's theorem KH-5 Argon Geodesic Mapping Geodesic diffeomorphism Geodesic function Geodesic mapping
is Wikipage redirect of	Geodesic Mapping Geodesic diffeomorphism Geodesic function Geodesic mapping
is applications of	KH-5 Argon
is foaf:primaryTopic of	wikipedia-en:Geodesic_map

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