i have a new idea how to show that a periodic integral curve is a immersed submanifold, but i need a little help.

My Idea is the following:

if a,b)->M" alt="ca,b)->M" /> is a periodic integral curve with period p.

then i need to define a topology and a smooth structure on the image c(a,b), s.t. c(a,b) is a manifold and the inclusion map i:c(a,b)->M is a smooth immersion.

I think i need to define the topology, s.t. the maps and are diffeomorphisms. with sufficient small.

So we can define the topology as: is open, if , is open in (a,b).

Then and and the corresponding inverse maps are all continuous.

And the smooth structure can be defined as

if then we can choose the coordinate system with \phi a coordinate

and analog if q=c(p).

Do you mean, that this is enough or right??

Regards