• IntroductionMetric tensor
  • IntroductionArc lengthCoordinate transformationsInvariance of arclength under coordinate transformationsLength and angleArea
  • Definition
  • Components of the metricMetric in coordinatesSignature of a metricInverse metricRaising and lowering indicesInduced metric
  • Intrinsic definitions of a metricMetric as a section of a bundleMetric in a vector bundleTangent–cotangent isomorphism
  • Arclength and the line elementThe energy, variational principles and geodesics
  • Canonical measure and volume form
  • ExamplesEuclidean metricThe round metric on a sphereLorentzian metrics from relativity
  • See also
  • Notes
  • References