- 3
- 0
I'm trying to work up some examples to help me understand this concept. Would the periodic flow on a solid torus be transverse to it's boundary?
Transverse to the boundary means that the part of the flow that is on boundary does not lie in the tangent space to the boundary. So the flow must point either outwards or inwards.So since it's a periodic flow, say given by $$dx = -y, dy=x \mbox{ and }dz = 0,$$ all trajectories are parallel to the boundary, so they would not lie in the tangent space to any boundary points, and the flow would be transverse?
First of all, there are a lot of different periodic flows on a solid torus, so no one flow is "the" periodic flow.*I'm trying to work up some examples to help me understand this concept. Would the periodic flow on a solid torus be transverse to it's boundary?