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- Geodesic_curvature abstract "In Riemannian geometry, the geodesic curvature of a curve measures how far the curve is from being a geodesic. In a given manifold , the geodesic curvature is just the usual curvature of (see below), but when is restricted to lie on a submanifold of (e.g. for curves on surfaces), geodesic curvature refers to the curvature of in and it is different in general from the curvature of in the ambient manifold . The (ambient) curvature of depends on two factors: the curvature of the submanifold in the direction of (the normal curvature ), which depends only from the direction of the curve, and the curvature of seen in (the geodesic curvature ), which is a second order quantity. The relation between these is . In particular geodesics on have zero geodesic curvature (they are "straight"), so that , which explains why they appear to be curved in ambient space whenever the submanifold is.".
- Geodesic_curvature wikiPageID "483526".
- Geodesic_curvature wikiPageRevisionID "602919459".
- Geodesic_curvature first "Yu.S.".
- Geodesic_curvature hasPhotoCollection Geodesic_curvature.
- Geodesic_curvature id "G/g044070".
- Geodesic_curvature last "Slobodyan".
- Geodesic_curvature title "Geodesic curvature".
- Geodesic_curvature urlname "GeodesicCurvature".
- Geodesic_curvature year "2001".
- Geodesic_curvature subject Category:Geodesic_(mathematics).
- Geodesic_curvature subject Category:Manifolds.
- Geodesic_curvature comment "In Riemannian geometry, the geodesic curvature of a curve measures how far the curve is from being a geodesic. In a given manifold , the geodesic curvature is just the usual curvature of (see below), but when is restricted to lie on a submanifold of (e.g. for curves on surfaces), geodesic curvature refers to the curvature of in and it is different in general from the curvature of in the ambient manifold .".
- Geodesic_curvature label "Geodesic curvature".
- Geodesic_curvature label "Geodetische kromming".
- Geodesic_curvature label "Geodätische Krümmung".
- Geodesic_curvature label "测地曲率".
- Geodesic_curvature sameAs Geodätische_Krümmung.
- Geodesic_curvature sameAs Geodetische_kromming.
- Geodesic_curvature sameAs m.02fz6r.
- Geodesic_curvature sameAs Q1460595.
- Geodesic_curvature sameAs Q1460595.
- Geodesic_curvature wasDerivedFrom Geodesic_curvature?oldid=602919459.
- Geodesic_curvature isPrimaryTopicOf Geodesic_curvature.