About: Riemannian circle

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In metric space theory and Riemannian geometry, the Riemannian circle is a great circle equipped with its great-circle distance. It is the circle equipped with its intrinsic Riemannian metric of a compact one-dimensional manifold of total length 2π, or the extrinsic metric obtained by restriction of the intrinsic metric on the sphere, as opposed to the extrinsic metric obtained by restriction of the Euclidean metric to the unit circle in the plane. Thus, the distance between a pair of points is defined to be the length of the shorter of the two arcs into which the circle is partitioned by the two points.

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rdfs:label	Riemannian circle
rdfs:comment	In metric space theory and Riemannian geometry, the Riemannian circle is a great circle equipped with its great-circle distance. It is the circle equipped with its intrinsic Riemannian metric of a compact one-dimensional manifold of total length 2π, or the extrinsic metric obtained by restriction of the intrinsic metric on the sphere, as opposed to the extrinsic metric obtained by restriction of the Euclidean metric to the unit circle in the plane. Thus, the distance between a pair of points is defined to be the length of the shorter of the two arcs into which the circle is partitioned by the two points.
foaf:depiction
foaf:isPrimaryTopicOf	wikipedia-en:Riemannian_circle
thumbnail	wiki-commons:Special:FilePath/Sphere_halve.png?width=300
dct:subject	Circles Bernhard Riemann Riemannian geometry Metric geometry
Wikipage page ID	19371215(xsd:integer)
Wikipage revision ID	955094778(xsd:integer)
Link from a Wikipage to another Wikipage	Unit circle Diameter Differential geometry Great circle Circles Riemannian geometry Filling area conjecture Gaussian curvature Germans Embedding Bernhard Riemann Mathematician Bernhard Riemann Mikhael Gromov (mathematician) Length Riemannian manifold Metric space Riemannian geometry Metric geometry Plane (geometry) Euclidean distance Hilbert space Great-circle distance
sameAs	Riemannian circle Riemannian circle Riemannian circle Riemannian circle Riemannian circle
dbp:wikiPageUsesTemplate	dbt:Clarify dbt:Pi
has abstract	In metric space theory and Riemannian geometry, the Riemannian circle is a great circle equipped with its great-circle distance. It is the circle equipped with its intrinsic Riemannian metric of a compact one-dimensional manifold of total length 2π, or the extrinsic metric obtained by restriction of the intrinsic metric on the sphere, as opposed to the extrinsic metric obtained by restriction of the Euclidean metric to the unit circle in the plane. Thus, the distance between a pair of points is defined to be the length of the shorter of the two arcs into which the circle is partitioned by the two points. It is named after German mathematician Bernhard Riemann.
prov:wasDerivedFrom	wikipedia-en:Riemannian_circle?oldid=955094778&ns=0
page length (characters) of wiki page	1938(xsd:integer)
is foaf:primaryTopic of	wikipedia-en:Riemannian_circle
is Link from a Wikipage to another Wikipage of	Unit circle Great circle Riemannian Circle Sphere Area Intrinsic metric List of circle topics Great-circle distance List of things named after Bernhard Riemann Pu's inequality
is Wikipage disambiguates of	Riemannian

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