Torsion Tensor

The torsion tensor is a tensor associated with an affine connection on a manifold that measures the failure of infinitesimal parallelograms formed by parallel transport to close up, equivalently the antisymmetric part of the connection's coefficients. A connection with zero torsion, such as the Levi-Civita connection used in standard Riemannian geometry, is called torsion-free, and most classical differential geometry works with torsion-free connections. Nonzero torsion appears in more general geometric frameworks, including certain formulations of gravitational theory that generalize general relativity to allow spacetime torsion alongside curvature. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/