Revision #152 → #1261 · back to history
addedGeodesic (locally shortest path)8b200bdae8fd
addedVanishing geodesic curvature characterizationc033358c2048
addedGeodesic via length minimizationbf56760523ac
addedNon-uniqueness of distance minimizersd2e7afbc5835
addedSegment of a geodesic is a geodesic430cf7c62892
addedGeodesics are only locally shortest4d26bf410eb9
addedLong way round on a great circle49511171a82d
addedReparameterized unit-interval map is not a geodesic928c3650a5e2
addedStraight lines in Euclidean geometryab0673042324
addedGreat circles on a spherefde5def26e43
addedAntipodal points: infinitely many shortest pathsd247320409e4
addedGeodesics on an ellipsoiddd622ab27147
addedGeodesic triangle23c53fc2c354
addedSpherical triangleb9ee6eb030b7
addedGeodesic in metric geometrycced8224a42c
addedMinimizing geodesic / shortest path3f5d085f912e
addedMetric space may have no geodesicsabe077f400cc
addedLength space: minimizing sequence of paths5294ae051102
addedMetric Hopf–Rinow theorem9e3cb68b002b
addedGeodesic metric spaces that are not manifoldse8bf4f99aebe
addedLength of a curve5d5bf0efd5c6
addedRiemannian distance2abbe39c6805
addedGeodesics are locally distance-minimizing (converse false)c31c78920b7d
addedCharacterization of geodesics among minimizers6903b5914829
addedEnergy functional definition of geodesics342d948317ec
addedCauchy–Schwarz length/energy inequalitya2fe70bf2cab
addedEnergy minimizers also minimize length8ad768f60e88
addedGeodesic equation (Euler–Lagrange)8d79770a6973
addedFirst variation of energy2eadf9c9088e
addedCritical points of first variation are geodesicsd4516153eb09
addedSecond variationa56362f10798
addedZeros of second variation are Jacobi fields990f529c0ee4
addedGeodesics as Hamiltonian flowsbb79984182a3
addedAffine geodesic (parallel transport)1f0dd3c69452
addedUnique solution from initial position and velocity577992928865
addedLocal existence and uniqueness of geodesicsa14ad7132bb0
addedGeodesic completenesscd0b3f381e2a
addedGeodesic flowfeb88a3173f2
addedClosed orbit = closed geodesic927d41f9fec3
addedGeodesic flow as Hamiltonian flow93c396ad82d2
addedGeodesic flow preserves the metric21e2f703554d
addedLiouville's theorem: invariance of kinematic measure58999b6804c1
addedGeodesic spray1ad447b55dd3
addedSplitting of double tangent bundle0ccbfb5e9ea2
addedGeodesic spray as unique horizontal vector field8ad7ad694076
addedSpray from rescaling-equivariant connection3d43597a9820
addedInvariance under affine reparameterization6285f4fb164c
addedGeodesics with affine parameterf86f6bdbac37
addedConnection determined by geodesics up to torsionbba101cb9a29
addedSkew-symmetric difference tensor gives same geodesics80fcb1c15fac
addedUnique torsion-free connection with same geodesics173cb13dae04
addedProjective connection998fa6ee26b6
addedRibbon testb28bfa401693
addedRibbon around a cone9f7aeaeeee1c
addedMathematical formulation of ribbon test9105db4cf9b3
addedUnique closed geodesic per homotopy class1710cd69ea4a