- #1
center o bass
- 560
- 2
Suppose we have a torsion free connection. Does anyone here know of a slick way to prove that covariant derivatives satisfy the Jacobi identity? I.e. that
$$([\nabla_X,[\nabla_Y,\nabla_Z]] + [\nabla_Z,[\nabla_X,\nabla_Y]] +[\nabla_Y,[\nabla_Z,\nabla_X]])V = 0$$
without going into coordinate basis.
$$([\nabla_X,[\nabla_Y,\nabla_Z]] + [\nabla_Z,[\nabla_X,\nabla_Y]] +[\nabla_Y,[\nabla_Z,\nabla_X]])V = 0$$
without going into coordinate basis.