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The Riemann manifold curvature tensor for geometry fans

Let’s start with the basics. The curvature tensor is a measure of how curved a surface is at each point. Mathematically, it was first defined in tensor calculus by Bernhard Riemann in 1854. In mathematics, the curvature tensor is an important two-dimensional sub-tensor of the rank-2 tensor called the metric tensor and describes how space …

The Riemann curvature tensor

In mathematics, the Riemann curvature tensor is a mathematical object that measures the local curvature of a surface near each point on it. The curvature tensor is the 2nd order Riemann-Christoffel tensor, which can also be expressed as an antisymmetric 2×2 matrix. It is defined in 3-dimensional Euclidean space by where A, B, and C …