Revision #601 → #1404 · back to history
addedMetric tensor (informal)537409d51fa4
addedPositive-definite metric tensor and Riemannian manifold11700537ee32
addedMetric tensor as covariant symmetric tensor61ba2e4b2938
addedParametric surfacee35b013f5ae8
addedArc length on a parametric surface01e23096e607
addedLine element and first fundamental formaf23728236c9
addedMetric tensor of a surface (via transformation law)8a12eb8159ba
addedInvariance of first fundamental form under coordinate changecb74af68995a
addedInner product of tangent vectors via metric3fb2bc22424b
addedSymmetry and bilinearity of the surface metricead753685a90
addedLength of a tangent vectorbdaf56a2f87f
addedAngle between tangent vectors64719687a34d
addedSurface area via parameterization943065c1a13c
addedSurface area via determinant (Lagrange's identity)2d7845156cb6
addedMetric tensor at a point255b0fd9650b
addedMetric tensor field on a manifold7a8a90bc4e39
addedComponents of the metric in a frameef78274934d6
addedCovariant transformation of metric components01c30c4b96ba
addedMetric components in coordinates21ed547b46e8
addedTransformation of metric components under coordinate change6f06218f2301
addedPositive-definite metric and Riemannian metric74b79ee931fb
addedPseudo-Riemannian metric and signature7c678494bac3
addedSylvester's law of inertia for metric diagonalizationf43b68127d21
addedSignature is constant on connected manifold36ea7e438d81
addedSignature of a metric7d4aec959128
addedLorentzian and ultrahyperbolic metricsf1ad6b6e3fd6
addedInverse metrice1ead45a197a
addedContravariant transformation of inverse metric4cdd8c5b0ba4
addedBasis-independence of inverse metric on covectors1792d481cf5d
addedLowering the index5d1ffc1442b5
addedRaising the index102f87b0a060
addedImmersion and immersed submanifold6bdef46bf539
addedFirst fundamental form (induced metric in ℝ³)dfe8f120ae1d
addedPushforward of a tangent vectorda018949b8b0
addedInduced metric4f12d8e4c370
addedMatrix form of induced metric via Jacobian27dbd00790a7
addedIntrinsic metric tensor via fiber bundles53397cfc7655
addedMetric as section of dual tensor product bundle1b456face730
addedSymmetry of g⊗ as tensor504354ac5951
addedMetric in a vector bundle2268851a5fae
addedMusical isomorphism (tangent–cotangent)fe51d2eb6084
addedS_g is a symmetric linear isomorphismf32367054dda
addedCorrespondence between symmetric bilinear forms and symmetric isomorphisms34f2255ec5b5
addedArclength of a parametric curve on a Riemannian manifold5f029ec45a4c
addedFirst fundamental form and line element1d29f5c39000
addedCoordinate-independence of length formulas8a7153fb9534
addedEnergy of a curveeeac9950ca92
addedGeodesic equations from variational principlese4f842f44752
addedCanonical Borel measure from metric tensor7ab96bc6a7d0
addedVolume form on an oriented Riemannian manifoldfae959b57ba6
addedTwo-dimensional Euclidean metriccd8b9a5422a3
addedEuclidean metric in polar coordinatesb20b246179a1
addedEuclidean metric in curvilinear coordinatesfd05f5f64fce
addedRound metric on the sphere872765ed7bc8
addedMinkowski metric (special relativity)00199931a282
addedSchwarzschild metric3593260d03a8