Mathematical Physics


Simplified Calculation of Component Number in the Curvature Tensor

Authors: William O. Straub

The number of independent components in the Riemann-Christoffel curvature tensor, being composed of the metric tensor and its first and second derivatives, varies considerably with the dimension of space. Since few texts provide an explicit derivation of component number, we present here a simplified method using only the curvature tensor’s antisymmetry property and the cyclicity condition. For generality and comparison, the method for computing component number in both Riemannian and non-Riemannian space is presented.

Comments: 2 Pages.

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Submission history

[v1] 2015-03-21 12:54:48

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