info prev up next book cdrom email home

Bianchi Identities

The Riemann Tensor is defined by


\begin{displaymath}
R_{\lambda\mu\nu\kappa;\eta} = {1\over 2}{\partial\over\part...
...^2g_{\mu\kappa}\over\partial x^\nu\partial x^\lambda}}\right).
\end{displaymath}

Permuting $\nu$, $\kappa$, and $\eta$ (Weinberg 1972, pp. 146-147) gives the Bianchi identities

\begin{displaymath}
R_{\lambda\mu\nu\kappa;\eta}+R_{\lambda\mu\eta\nu;\kappa} +R_{\lambda\mu\kappa\eta;\nu}=0.
\end{displaymath}

See also Bianchi Identities (Contracted), Riemann Tensor


References

Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: Wiley, 1972.




© 1996-9 Eric W. Weisstein
1999-05-26