General Relativity: An Introduction for Physicists · Problem 4.4

Tensor calculus on manifolds — Hobson, Efstathiou & Lasenby

Physics · symmetric-tensor-vector-vanishing

Problem

t_{ab}

are the components of a symmetric tensor and

v_a

the components of a vector, show that if

v_a t_{bc} + v_c t_{ab} + v_b t_{ca} = 0

then either

t_{ab} = 0

v_a = 0