Revision #914 → #1543 · back to history
addedRiemannian manifold (informal)8f489a8ac27e
addedRiemannian metric (informal)a54850aeefc7
addedTheorema Egregium33041a26c564
addedLocal isometry (surfaces)c2055187b47b
addedIntrinsic/extrinsic propertya713aeb65d6a
addedRiemannian metric and Riemannian manifolde5873192f9b0
addedMetric components in coordinatesc9d2a2980add
addedContinuous/smooth Riemannian metric31459bcceb44
addedMusical isomorphism7d805eedbdd5
addedIsometry944442fb5605
addedLocal isometry7cbcb2601679
addedRiemannian volume formc4194010724b
addedEuclidean metricbf6af90d7432
addedRiemannian submanifolddbd786d7968d
addedRound metric on the sphere11c8cae37637
addedEllipsoid as submanifoldb73e482cfb25
addedGraph of smooth function85ba61b72989
addedCovering space inherits metric08cb80b46618
addedIsometric immersion/embeddinge5ed66c3c8cf
addedProduct Riemannian metric169c939d49f8
addedFlat torusc8404234c778
addedPositive combinations of metricsedcae84901d7
addedExistence of Riemannian metric40ba7cadcc2f
addedNash embedding theorem9739c3853f35
addedAdmissible curve and lengthb7b2cc5ecf22
addedRiemannian distance is a metric6a1a9fe3536b
addedDiameter49115a34eab4
addedCompactness iff finite diameter (complete)f00e371f344e
addedAffine connection3a218351b067
addedCovariant derivative7a3f66b1d0c3
addedMetric-preserving connectionddd759c2b339
addedTorsion-free connection240091057396
addedLevi-Civita connection existence/uniqueness2dfcff3c05eb
addedVector field along a curve6ee36a88f485
addedExtension of vector field along curve8924133b91ba
addedCovariant derivative along a curve0409620e858c
addedGeodesicdb343c134220
addedExistence and uniqueness of geodesicsf88ba9f8e0b4
addedMaximal geodesic8080b5e738c4
addedShortest curves are geodesics0d8cf058dc88
addedGeodesics in the Euclidean plane1aef34fa098e
addedGeodesics on the sphere8714e64bc491
addedGeodesically complete1878b5dc0353
addedHopf–Rinow theorem495aa58e4b6f
addedParallel vector fielde3c779515c3d
addedParallel transport315bdcc1d773
addedRiemann curvature tensor32d0d2eb4d30
addedVanishing curvature iff locally Euclidean7234eca45be6
addedRicci curvature tensor8b8f9fa879d9
addedEinstein metric / Einstein manifold339fbf46408c
addedConstant curvature4f09d256d55e
addedConstant curvature implies Einsteinf781e34fc019
addedRiemannian space form4f56a1bbdf6b
addedKilling–Hopf theorem2d19f141a247
addedLeft-invariant metric on Lie groupfff138786d08
addedBi-invariant metric existence67212202f752
addedHomogeneous Riemannian manifold6092325a24c6
addedHomogeneous implies geodesically complete6a594da2c18c
addedClassification of homogeneous Riemannian manifolds8cdd0bcab58d
addedSymmetric Riemannian manifoldbee20dd180e2
addedCartan: locally symmetric implies symmetrica220e1650d32
addedBerger's holonomy classification35015a6ed188
addedWeak/strong Riemannian metricd640181d4a27
addedHilbert space strong metricfa761a441e63
addedL² weak metric on diffeomorphism groupc69f0fa06343
addedStrong metric separates points2bac47e40d4b
addedVanishing geodesic distance for weak metric01b99036b8ed
addedHopf–Rinow (strong, infinite-dim)c588a1456cac