## partial derivative of metric tensor

v r ( On a Riemannian manifold, the curve connecting two points that (locally) has the smallest length is called a geodesic, and its length is the distance that a passenger in the manifold needs to traverse to go from one point to the other. When that varies in a smooth (or differentiable) manner from point to point. In the above coordinates, the matrix representation of η is, (An alternative convention replaces coordinate The resulting natural positive Borel measure allows one to develop a theory of integrating functions on the manifold by means of the associated Lebesgue integral. 0 M t to give a real number: This is a generalization of the dot product of ordinary Euclidean space. DefMetric@1,metrich@-a,-bD,cd, 8"È","D"<,InducedFrom® 8metricg,n<,PrintAs->"h"D. DefMetric::old : There are already metrics 8metricg

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