About: Clifton–Pohl torus

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In geometry, the Clifton–Pohl torus is an example of a compact Lorentzian manifold that is not geodesically complete. While every compact Riemannian manifold is also geodesically complete (by the Hopf–Rinow theorem), this space shows that the same implication does not generalize to pseudo-Riemannian manifolds. It is named after Yeaton H. Clifton and William F. Pohl, who described it in 1962 but did not publish their result.

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rdfs:label	Clifton–Pohl torus (en)
rdfs:comment	In geometry, the Clifton–Pohl torus is an example of a compact Lorentzian manifold that is not geodesically complete. While every compact Riemannian manifold is also geodesically complete (by the Hopf–Rinow theorem), this space shows that the same implication does not generalize to pseudo-Riemannian manifolds. It is named after Yeaton H. Clifton and William F. Pohl, who described it in 1962 but did not publish their result. (en)
dcterms:subject	Lorentzian manifolds
Wikipage page ID	34242725 (xsd:integer)
Wikipage revision ID	1104398505 (xsd:integer)
Link from a Wikipage to another Wikipage	Homothetic transformation Hopf–Rinow theorem Isometry (Riemannian geometry) Compact space Geodesic Geometry Conjugate points Lorentzian manifold Torus William Francis Pohl Isometry group Riemannian manifold Group action (mathematics) Lorentzian manifolds E. Hopf Geodesically complete Null geodesic
sameAs	Clifton–Pohl torus Clifton–Pohl torus Clifton–Pohl torus
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	In geometry, the Clifton–Pohl torus is an example of a compact Lorentzian manifold that is not geodesically complete. While every compact Riemannian manifold is also geodesically complete (by the Hopf–Rinow theorem), this space shows that the same implication does not generalize to pseudo-Riemannian manifolds. It is named after Yeaton H. Clifton and William F. Pohl, who described it in 1962 but did not publish their result. (en)
gold:hypernym	Example
prov:wasDerivedFrom	wikipedia-en:Clifton–Pohl_torus?oldid=1104398505&ns=0
page length (characters) of wiki page	4713 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Clifton–Pohl_torus
is Link from a Wikipage to another Wikipage of	Hopf–Rinow theorem Geodesic manifold William Francis Pohl Pseudo-Riemannian manifold Clifton-Pohl torus
is Wikipage redirect of	Clifton-Pohl torus
is foaf:primaryTopic of	wikipedia-en:Clifton–Pohl_torus

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