Let M be a manifold
I want to show, that the integral curves of a vector field V are immersed submanifolds of M.
We assume that the vector field V doesn't vanish anywhere.
I could show that any integral curve is a immersion.
If the integral curve c is also injective, that is c is an injective immersion then the image of c is a immersed submanifold.
But what happens if c isn't injective. For instance if c is periodic?
How can i show that the image of c is a immersed submanifold, i.e. the inclusion map i: c(a,b)->M is a smooth immersion?
Please help me!
Thanks in advance