| Topic: |
Science > Physics |
| User: |
"Dr Tim" |
| Date: |
02 Mar 2006 01:57:19 AM |
| Object: |
u_r;s + u_s;r = 0 |
I'm investigating vector fields on curved manifolds that satisfy
u_r;s + u_s;r = 0
In other words, the gradient matrix is antisymmetric.
Is there a name for this equation?
Is there a name for solutions to this equation?
This is a linear equation, so its solutions form a vector space.
My intuition is that this vector space has finite dimension.
(ie there are only finitely many linearly independent solutions)
For four dimension space, I suspect that there are only ten independent
solutions.
Is anything known about this?
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