General Relativity: An Introduction for Physicists · Problem 4.3

Tensor calculus on manifolds — Hobson, Efstathiou & Lasenby

Physics · antisymmetric-tensor-vector-identity

Problem

t_{ab}

are the components of an antisymmetric tensor and

v_a

the components of a vector, show that

v_{[a}t_{bc]} = \tfrac{1}{3}(v_a t_{bc} + v_c t_{ab} + v_b t_{ca}).