Hello,

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