General Relativity: An Introduction for Physicists · Problem 4.5

Tensor calculus on manifolds — Hobson, Efstathiou & Lasenby

Physics · tensor-symmetry-identity

Problem

If the tensor

t_{abcd}

satisfies

t_{abcd}v^a w^b v^c w^d = 0

for arbitrary vectors

v^a

and

w^a

, show that

t_{abcd} + t_{cdab} + t_{cbad} + t_{adcb} = 0.