Proving the symmetry property of Riemann curvature tensor

  • #1
Wan
3
0

Homework Statement


Hi everyone! Just wondering if there's a way to prove the symmetry property of the Riemann curvature tensor $$ R_{abcd} = R_{cdab}$$ without using the anti-symmetry property $$ R_{abcd} = -R_{bacd} = -R_{abdc} $$? I'm only able to prove it with the anti-symmetry property and cyclic property.

Thanks!

2. Homework Equations

None

The Attempt at a Solution


I tried subbing in the definition of the curvature tensor but it didn't work. I've already done this homework question but am just wondering if there are other methods to do it.
 

Answers and Replies

  • #2
12,520
6,310

Related Threads on Proving the symmetry property of Riemann curvature tensor

Replies
8
Views
3K
Replies
0
Views
2K
  • Last Post
Replies
1
Views
356
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
16
Views
4K
Replies
0
Views
3K
Replies
1
Views
593
Replies
4
Views
4K
  • Last Post
Replies
1
Views
365
Replies
4
Views
866
Top