Riemannian manifold

In Riemannian geometry, a Riemannian manifold (M, g) is a real differentiable manifold M in which each tangent space is equipped with an inner product < , > in a manner which varies smoothly from point to point. This allows one to define of various notions as the length of curves, angles, areas (or volumes), curvature, gradients of functions and divergence of vector fields.

Related Topics:
Riemannian geometry - Manifold - Tangent space - Inner product - Curve - Angle - Area - Volume - Curvature - Gradient - Divergence - Vector field

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