Riemannian Metric

Suppose for every point x in a manifold M, an inner product <·,·>_x is defined on a tangent space T_xM of M at x. Then the collection of all these inner products is called the Riemannian metric. In 1870, Christoffel and Lipschitz showed how to decide when two Riemannian metrics differ by only a coordinate transformation.

See also

Compact Manifold, Line Element, Metric Tensor, Minkowski Metric, Riemannian Geometry, Riemannian Manifold

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Cite this as:

Weisstein, Eric W. "Riemannian Metric." From MathWorld--A Wolfram Web Resource.

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