- #1
Telemachus
- 835
- 30
Hi there. This is my first time working with tensors, so I have to break the ice I think. I have this exercise, which I don't know how to solve, which says:
If [tex]V=V_1...V_n[/tex] is a first order covariant tensor, prove that:
[tex]T_{ik}=\frac{\partial V_i}{\partial x^k}-\frac{\partial V_k}{\partial x^i}[/tex]
Is a second order covariant antisymmetric tensor.
Now, in my notes I have this definitions:
A vector field V is a first order covariant tensor, if under a change of coordinates from [tex]x[/tex] to [tex]\overline x[/tex] it's components are:
[tex]\overline {V}=\frac{\partial x^r}{\partial \overline {x}^i}V_r[/tex]
I think I should use this, but as I said, I'm starting with this, and I don't know how to work this out.
Any help will be appreciated.
If [tex]V=V_1...V_n[/tex] is a first order covariant tensor, prove that:
[tex]T_{ik}=\frac{\partial V_i}{\partial x^k}-\frac{\partial V_k}{\partial x^i}[/tex]
Is a second order covariant antisymmetric tensor.
Now, in my notes I have this definitions:
A vector field V is a first order covariant tensor, if under a change of coordinates from [tex]x[/tex] to [tex]\overline x[/tex] it's components are:
[tex]\overline {V}=\frac{\partial x^r}{\partial \overline {x}^i}V_r[/tex]
I think I should use this, but as I said, I'm starting with this, and I don't know how to work this out.
Any help will be appreciated.