Question

Show that the tensor

$T_{\mu\nu\rho\sigma} = g_{\mu\rho}g_{\nu\sigma} - g_{\mu\sigma}g_{\nu\rho}$

defined from the metric tensor  $g_{\mu\nu}$ satisfies the symmetry property

$T_{\mu\nu\rho\sigma} = -T_{\nu\mu\rho\sigma} = -T_{\mu\nu\sigma\rho} = T_{\rho\sigma\mu\nu}$

Evaluate the contracted tensors

$U_{\mu\nu} = {T_{\mu\nu\rho}}^{\rho},$ and  $W_{\mu\rho} = {T_{\mu\nu\rho}}^{\nu}$

in four dimensions and in general n dimensions

Answer 1

ap T. Ca loul an

Hv. ㄒ

7,小 ? 39ん1