- #1
schieghoven
- 85
- 1
Under what circumstances do we know whether a given tensor of 4th rank could be the curvature tensor of a manifold? For instance, if I specify some arbitrary functions R_{ijkl} (with the necessary symmetries under interchange i<->j, k<->l, and ij<->kl), is it necessarily the case that there is a manifold for which R_{ijkl} is the curvature? I guess that satisfying the Bianchi identities is a necessary precondition.
And if so, is there any way to construct the metric explicitly?
Thanks,
Dave
And if so, is there any way to construct the metric explicitly?
Thanks,
Dave