Linked from

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

• GeodesicRelated: The metric determines which paths count as geodesics.

• Differential geometryBroader topic: It defines lengths, angles, and distances on the spaces studied in Riemannian geometry.

• Differential formCompared with: A metric pairs vectors and measures lengths; forms are covariant alternating tensors.

• Tangent spaceRelated: It measures lengths and angles of tangent directions.

• Riemannian geometryBroader topic: It supplies the lengths and angles that define Riemannian geometry.

• Gaussian curvatureNarrower topic: Gaussian curvature is the two-dimensional curvature determined by this intrinsic metric.

• Hessian matrixCompared with: A metric describes geometric lengths, whereas a Hessian describes function curvature.

• Riemannian manifoldBroader topic: This is the additional structure that turns a smooth manifold into a Riemannian one.

• Gauss–Bonnet theoremRelated: A metric supplies the lengths and curvature integrated by the theorem.

• Exponential mapRelated: A metric induces the Levi-Civita connection used to define Riemannian geodesics.

• Ricci curvatureRelated: The metric determines the connection and curvature from which Ricci curvature is formed.

• Levi-Civita connectionRelated: It is the geometric data the connection preserves.

• Partition of unityRelated: Local metrics can be averaged with partition functions to produce a global metric.

• Tensor fieldBroader topic: It is a symmetric covariant tensor field that measures lengths and angles.

• Bilinear formRelated: Each tangent space carries a bilinear form that defines lengths and angles.

• Ricci flowBroader topic: The evolving metric is the geometric quantity Ricci flow changes.

• Riemannian distanceNarrower topic: It assigns the lengths of tangent vectors used to measure curves.

• Geometric analysisBroader topic: Metrics turn a smooth manifold into a measurable geometric space.

• Flat torusNarrower topic: A flat torus is defined by equipping its underlying surface with this structure.

• Systolic geometryNarrower topic: Systolic lengths and volumes are measured using a Riemannian metric.

• Clairaut's relationNarrower topic: The metric defines the geodesics and angle measured in Clairaut's relation.

• Filling area conjectureNarrower topic: The conjecture can be framed for disks whose intrinsic geometry is specified by a metric.

• Gauss's lemma (differential geometry)Narrower topic: The lemma concerns orthogonality measured by this metric after tangent vectors are mapped onto the manifold.