Definition of Tensor Identity Simplification

[Arman777]

Is there a simplifcation of $g^{\alpha \delta}g_{\beta \gamma}$ or what is equal to ?

 

[etotheipi]

it's just a coordinate dependent number no? assuming your indices are not abstract or anything

 

[Arman777]

Okay I got no worries

 

[PeterDonis]

Is there a simplifcation of $g^{\alpha \delta}g_{\beta \gamma}$ or what is equal to ?

Not if all the indexes are different.

Also, what does this have to do with a tensor density?