Let $M^3$ be a complete riemannian manifold and $\Sigma ^2\subset M^3$ a embedded minimal compact surface. Consider the normal variation $\phi: \Sigma \times \Bbb{R}\to M$ given by

$$\phi(p,t)=\exp_p(tN(p)),$$

when $N$ is a normal vector field along to $\Sigma.$

I want to show that:

**Lemma:** There is $\delta>0$ such that $\phi:\Sigma\times [0,\delta) \to M$ is an immersion and even an embedding on $\Sigma\times [0,\delta)$.

I tried a sketch with tubular neighborhood tecniques but I don't conclude anything in this direction. In fact, I know that there is the tubular neighborhood of $\Sigma$, but I don't know how immerse this in $M$.

Anyone has a little help?

Thanks so much.