Hello all,(adsbygoogle = window.adsbygoogle || []).push({});

I have been given a problem where I am asked to calculate "all" the components of the Riemann tensor in a gross non-diagonalized metric. I know there exists at most 20 independent components of Riemann, but I want to actually compose a list of these combinations.

It is easy enough to generate a good quantity of combinations which don't vanish under the antisymmetric exchange, but it is a bit harder to do this and account for the first Bianchi Identity. I made a list of 21 components which I should have to calculate and their could exist more but I realized I have no idea how to figure out how many more I need since there may be redundancies in my current list.

To reiterate; I was wondering if there was a compiled list somewhere for 20 independent components.

Thanks

--Ozone.

PS: If anyone could help me to figure out what the difference in the # of components with the Bianchi Identity applied and with just the block identity//antisymmetry of the Riemann that would be much appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Does an explicit list of 20 independent compenents of Riemman exist?

**Physics Forums | Science Articles, Homework Help, Discussion**