Скачать или смотреть General Relativity - General Tensors : Covariant Riemann Curvature Tensor

The covariant Riemann curvature tensor plays a significant role in general relativity.It’s a foundational concept of differential geometry and general relativity. Basically it’s defined as the inner product of the mixed Riemann tensor and the covariant fundamental tensor. Here you will also see the basic properties of this Covariant Riemann Tensor. In general this tensor is represented by the symbol Rabcd. This Rabcd is anti symmetric in the first two indices and b. With respect to the last two indices c and d it’s also anti symmetric. It’s found that Rabcd is symmetric with respect to an interchange of the first and second pair pair of indices without changing the order of indices in each pair.It’s cyclic property has been also discussed.