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Differentiable Manifolds and Riemannian Metrics in Differential Geometry

A smooth manifold carries charts, a tangent space at each point and differentials of smooth maps between them; a Riemannian metric assigns a varying inner product to those tangent spaces, giving norms, angles, lengths of curves and geodesic distance. Compact boundaryless manifolds are the standard stage on which smooth dynamics is set.

Dr. Harry Seldon Video

Manifolds and Riemannian Metrics in Differential Geometry

A manifold is a topological space that is locally Euclidean: every point has a neighborhood that can be mapped via coordinates to an open subset of R^n, so that objects with global curvature can be a…