Скачать или смотреть General Relativity - General Tensors : Covariant Derivative of Fundamental Tensors

The covariant derivative is a generalization of the ordinary derivative that is compatible with curved space,such as those found in general relativity or differential geometry. It accounts for the curvature and coordinate dependence manifold. If a tensor is is of rank r then the covariant derivative of it is a tensor of order whose rank is r plus one. This process has a great importance in the study of general relativity. Einstein’s field equations use covariant derivatives to describe the curvature of spacetime. It has been shown that the covariant derivatives of fundamental tensors are zero,which implies that with respect to covariant differentiation all the three fundamental tensors can be treated as constants. This is why the fundamental tensors are defined as Covariant Constants.