Linked from

The 68 pages that link to Geodesic, each with the reason it gives.

• General relativityBroader topic: Freely falling bodies follow spacetime geodesics when nongravitational forces are absent.

• Differential geometryBroader topic: Geodesics generalize straight lines and reveal the metric’s local geometry.

• Non-Euclidean geometryRelated: Geodesics play the role of straight lines in curved geometries.

• Equivalence principleRelated: General relativity describes freely falling bodies as following paths through curved spacetime.

• GravityBroader topic: In general relativity, freely falling matter follows spacetime geodesics.

• SphereRelated: On a sphere, great-circle arcs are geodesics.

• Calculus of variationsBroader topic: Geodesics arise by extremizing curve length, a basic variational problem.

• Hyperbolic geometryRelated: Geodesics play the role of straight lines in hyperbolic geometry.

• Metric tensorRelated: The metric determines which curves are geodesics through its associated connection.

• Tangent spaceRelated: Its velocity lies in tangent spaces along the curve.

• Riemannian geometryRelated: Geodesics generalize straight lines and locally minimize distance.

• Spherical geometryNarrower topic: On a sphere, geodesics are arcs of great circles.

• SpacetimeRelated: Freely falling bodies follow geodesics in curved spacetime.

• Arc lengthRelated: Geodesics minimize path length under a space's geometry, unlike arbitrary arcs.

• Covariant derivativeRelated: Its defining equation sets the covariant derivative of the tangent along the curve to zero.

• DistanceBroader topic: On curved spaces, separation is measured along shortest paths constrained to the space.

• Free fallRelated: General relativity models freely falling bodies as following spacetime geodesics.

• Riemannian manifoldRelated: Geodesics generalize straight lines and locally extremize curve length.

• Riemannian metricBroader topic: The metric determines which curves count as locally straight.

• Great circleNarrower topic: Great circles are geodesics on a sphere.

• Proper timeRelated: In free fall, an ideal clock follows a timelike geodesic and locally maximizes elapsed proper time.

• Gravitational forceRelated: In general relativity, freely falling bodies follow spacetime geodesics rather than being pulled by a force.

• Smooth manifoldRelated: Geodesics generalize straight lines once a manifold has suitable geometric structure.

• Line segmentCompared with: A straight segment is the Euclidean case of a shortest path between two points.

• Map scaleRelated: For long distances, the ground distance may follow a curved-surface path rather than a flat line.

• Cayley graphRelated: Geodesics encode shortest generator expressions for group elements.

• Line (geometry)Related: In curved spaces, geodesics generalize straight lines.

• Spherical trigonometryRelated: On a sphere, great-circle arcs are geodesics and supply spherical-triangle sides.

• CurvatureRelated: Surface curvature influences how geodesics behave and converge.

• Minimal surfaceCompared with: Geodesics are the one-dimensional analogue of area-stationary surfaces.

• Affine connectionRelated: The connection determines which curves have tangent vectors that transport themselves parallelly.

• Exponential mapRelated: The map’s output is the point reached along a geodesic launched with the input vector.

• Elliptic geometryNarrower topic: Great-circle lines are geodesics in the spherical model.

• Levi-Civita connectionBroader topic: The connection's covariant derivative defines the equation for metric geodesics.

• Causal structureCompared with: Causal curves need not be geodesics, even when they connect events.

• Hamilton's principleRelated: Free-particle paths in suitable settings can be derived by extremizing an action.

• MeridianRelated: Meridians are geodesics on an ideal spherical Earth.

• Morse theoryRelated: Morse applied critical-point methods to the space of paths between points on a manifold.

• Nikolai LobachevskyRelated: Hyperbolic geometry treats geodesics as its straight lines.

• Oblate spheroidRelated: On an oblate spheroid, geodesics differ from great circles on a sphere.

• GravitationRelated: Freely falling bodies follow geodesics in general relativity.

• Hyperbolic planeBroader topic: Geodesics play the role of straight lines in this geometry.

• Rhumb lineNarrower topic: Rhumb lines are one family of paths on a sphere, distinct from its shortest geodesics.

• WorldlineRelated: Free-falling objects follow geodesic worldlines in general relativity.

• Great-circle distanceRelated: A great-circle arc is a geodesic on a sphere.

• Riemannian distanceRelated: Locally, geodesics realize the shortest lengths between sufficiently close points.

• Direct method in the calculus of variationsRelated: Energy minimization can establish the existence of geodesics under suitable geometric assumptions.

• PseudosphereRelated: Geodesics on the pseudosphere illustrate how straightest paths behave in negative curvature.

• Tullio Levi-CivitaRelated: The connection he defined determines geodesics in spaces equipped with a metric.

• Elliptic integralRelated: Geodesics on an ellipsoid lead to integrals reducible to elliptic forms.