Is this quantity a tensor and why?

[zouzou0]

T^{jk} = \frac{1}{\sqrt{g}}\frac{\partial}{\partial x^{i}} (\sqrt{g}B^{ijk})

Given B^{ijk} is a tensor
Find if T^{jk} is a tensor and explain why and if not what can be done to
B^{ijk} to make T^{jk} a tensor ?

I tried to solve this but i think i'am missing some rules !

I think T^{jk} looks like a div of B = B^{ijk},i
i tried to substitute B^{ijk},i with the derivative but i end up with a big quantity with christoffel symbols

any help please!

 

[dextercioby]

It's the divergence of a rank 3 (0,3) tensor which is a contraction from the covariant derivative of a tensor. Through contraction, the tensor/pseudo-tensor character is preserved, so...

 

[zouzou0]

thank you for the reply.
I found this and i guess it is your answer!

The divergence of a given contravariant tensor
results from the expression of the covariant
derivative of that tensor, and due to the contraction,
the divergence will be a tensor of a rank less by two
units.