Linked from

The 23 pages that link to Riemannian manifold, each with the reason it gives.

• Euclidean 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.

• Smooth manifoldBroader topic: It adds a metric, enabling lengths, angles, and curvature beyond smooth structure alone.

• ManifoldBroader topic: A Riemannian metric adds lengths, angles, and distances to a smooth manifold.

• Riemann surfaceCompared with: Its metric geometry differs from the conformal structure that defines a Riemann surface.

• 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.

• Symplectic manifoldCompared with: It measures lengths and angles, unlike a symplectic form's pairings.

• 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.

• Differentiable manifoldBroader topic: Adding a metric enables lengths, angles, curvature, and geodesics.

• Gromov–Hausdorff convergenceNarrower topic: Compact Riemannian manifolds are common inputs to Gromov–Hausdorff limit problems.

• Gromov's compactness theoremBroader topic: Sequences of such spaces are a central setting for geometric compactness arguments.

• 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.

• 3-manifoldCompared with: A 3-manifold is defined topologically and need not come with a metric or smooth structure.

• 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.