Coordinate basis vs local frame?

  • Thread starter pellman
  • Start date
  • #1
673
2

Main Question or Discussion Point

The wikipedia article on connection forms refers to a local frame. What is the relationship between local frames and coordinate bases? Are they the same thing? Is one a subset of the other?

The connection form article uses general notation [tex]e_\alpha[/tex] for the basis elements instead of the partial derivative notation [tex]\partial_\alpha[/tex] typically used for coordinate bases. Is it because not all bases are coordinate bases?
 

Answers and Replies

  • #2
Landau
Science Advisor
905
0
It is my understanding that 'local frame' is defined for any vector bundle (a basis of local sections), while the term 'coordinate frame' is reserved for the special case where the vector bundle is the tangent bundle of a smooth manifold, and the local frame is the usual basis of vector fields [itex]\{\frac{\partial}{\partial x^i}\}_i[/itex].
 
  • #3
673
2
To my own amazement, I actually get it. Thanks, Landau.
 

Related Threads on Coordinate basis vs local frame?

  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
2
Views
2K
Replies
10
Views
5K
Replies
14
Views
2K
Replies
6
Views
1K
Replies
40
Views
4K
Replies
5
Views
4K
Top