KnowraRiemannian manifoldLinked fromLinked fromThe 23 pages that link to Riemannian manifold, each with the reason it gives.All 23Broader topic 4Narrower topic 16Compared with 3Euclidean spaceNarrower topic: It generalizes Euclidean metric geometry to spaces that may be curved.Riemann curvature tensorNarrower topic: The tensor is defined on a manifold with a connection, commonly one induced by this metric.Ricci curvatureNarrower topic: Ricci curvature measures intrinsic geometry on this kind of manifold.Levi-Civita connectionNarrower topic: The Levi-Civita connection is defined for this metric geometry.Ricci flowNarrower topic: Ricci flow evolves metrics on this underlying geometric space.Riemannian distanceNarrower topic: Riemannian distance is defined between points of this geometric space.Chern–Gauss–Bonnet theoremNarrower topic: The metric supplies the curvature used in the theorem.Cartan–Hadamard theoremNarrower topic: The theorem concerns global geometry built from a Riemannian metric.Gromov–Hausdorff convergenceNarrower topic: Compact Riemannian manifolds are common inputs to Gromov–Hausdorff limit problems.Hopf–Rinow theoremNarrower topic: The theorem concerns the distance and geodesics induced by this structure.Hilbert's theoremNarrower topic: A surface's metric supplies the distances and completeness used in the theorem.Mostow rigidity theoremNarrower topic: Hyperbolic manifolds are Riemannian manifolds with constant negative curvature.Fundamental theorem of Riemannian geometryNarrower topic: The theorem applies to every such manifold.Hopf conjecture (Euler characteristic)Narrower topic: The conjecture concerns compact manifolds with this geometric structure.Myers's theoremNarrower topic: The theorem concerns global geometry induced by this smoothly varying metric.Soul theoremNarrower topic: The theorem concerns the global topology of spaces equipped with this geometric structure.
KnowraRiemannian manifoldLinked fromLinked fromThe 23 pages that link to Riemannian manifold, each with the reason it gives.All 23Broader topic 4Narrower topic 16Compared with 3Euclidean spaceNarrower topic: It generalizes Euclidean metric geometry to spaces that may be curved.Riemann curvature tensorNarrower topic: The tensor is defined on a manifold with a connection, commonly one induced by this metric.Ricci curvatureNarrower topic: Ricci curvature measures intrinsic geometry on this kind of manifold.Levi-Civita connectionNarrower topic: The Levi-Civita connection is defined for this metric geometry.Ricci flowNarrower topic: Ricci flow evolves metrics on this underlying geometric space.Riemannian distanceNarrower topic: Riemannian distance is defined between points of this geometric space.Chern–Gauss–Bonnet theoremNarrower topic: The metric supplies the curvature used in the theorem.Cartan–Hadamard theoremNarrower topic: The theorem concerns global geometry built from a Riemannian metric.Gromov–Hausdorff convergenceNarrower topic: Compact Riemannian manifolds are common inputs to Gromov–Hausdorff limit problems.Hopf–Rinow theoremNarrower topic: The theorem concerns the distance and geodesics induced by this structure.Hilbert's theoremNarrower topic: A surface's metric supplies the distances and completeness used in the theorem.Mostow rigidity theoremNarrower topic: Hyperbolic manifolds are Riemannian manifolds with constant negative curvature.Fundamental theorem of Riemannian geometryNarrower topic: The theorem applies to every such manifold.Hopf conjecture (Euler characteristic)Narrower topic: The conjecture concerns compact manifolds with this geometric structure.Myers's theoremNarrower topic: The theorem concerns global geometry induced by this smoothly varying metric.Soul theoremNarrower topic: The theorem concerns the global topology of spaces equipped with this geometric structure.