tensor field
assignment of a tensor continuously varying across a mathematical space
Killing tensor
symmetric (0,2)-tensor field T such that the total symmetrization of its covariant derivative vanishes
Ricci curvature
2-tensor obtained as a contraction of the Riemann curvature 4-tensor on a Riemannian manifold (or, more generally, a smooth manifold equipped with affine connection)
Lie derivative
derivative of a tensor field along the flow defined by a vector field
differential form
totally antisymmetric tensor field; section of exterior powers of the cotangent bundle
Cotton tensor
rank-3 tensor defined for a 3d (pseudo-)Riemannian manifold which measures the degree to which it fails to be conformally flat
torsion tensor
(1,2)-tensor field associated to an affine connection; characterizes "twist" of geodesics; if nonzero, geodesics will be helices
Riemann curvature tensor
tensor field in general relativity and geometry