Question

Define Metric coefficients.

Answer 1

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors v and w at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar g(v, w) in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

In the same way as a dot product, metric tensors are used to define the length of and angle between tangent vectors.

Through integration, the metric tensor allows one to define and compute the length of curves on the manifold.

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