| 释义 | 
		Riemannian MetricSuppose for every point   in a Compact Manifold  , an Inner Product   is defined on a Tangent Space   of   at  .  Then the collection of all these Inner Productsis called the Riemannian metric.  In 1870, Christoffel and Lipschitz showed how to decide when two Riemannian metricsdiffer by only a coordinate transformation. See also Compact Manifold, Line Element, Metric Tensor
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