conformal tensor

The Weyl tensor is the tensor C_(a b c d) defined by R_(a b c d) = C_(a b c d) + 2/(n - 2)(g_(a[c) R_d] b - g_(b[c) R_(d]a)) - 2/((n - 1)(n - 2)) R g_(a[c) g_(d]b), where R_(a b c d) is the Riemann tensor, R is the scalar curvature, g_(a b) is the metric tensor, and T_[a_1 ...a_n] denotes the antisymmetric tensor part. The Weyl tensor is defined so that every tensor contraction between indices gives 0.

Riemann tensor | scalar curvature