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.

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

• 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.

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