Covariant derivative

  • #1
Hello everyone,

While studying properties of Riemann and tensor and Killing vectors, I found this notation/concept that I'm not sure of it's meaning.

What does it mean to have a covariant derivative, using semi-colon notation, showing in upper index position. Is it just a matter of raising the index via the metric of ordinary covariant derivative.

I tried to search in different textbooks for this, but couldn't find anything.

Thanks in advance for your help.
 

Answers and Replies

  • #2
Ben Niehoff
Science Advisor
Gold Member
1,883
162
[tex]A^{ab;c} = g^{cd} \nabla_d A^{ab} = \nabla_d (g^{cd} A^{ab})[/tex]

Note that [itex]\nabla_c g_{ab} = 0[/itex].
 

Related Threads on Covariant derivative

Replies
3
Views
4K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
13
Views
6K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
3
Views
5K
Replies
3
Views
4K
Replies
26
Views
8K
Top