Nonmetricity tensor

The nonmetricity tensor is a mathematical object used in the context of a generalization of the theory of gravity, particularly in modifications of general relativity, such as in theories of metric-affine geometry. In differential geometry, the notion of nonmetricity is concerned with the way lengths and angles change under parallel transport. In the context of a connection on a manifold, the nonmetricity tensor is defined as the tensor that measures the failure of the connection to preserve the metric tensor during parallel transport.