I would like to find the answers to the following questions:

a.Find a complete $3$-dimensional Riemannian manifold $M$ and a point $p\in M$, such that the boundary of the open geodesic ball $B(p,1)$ is a smooth $2$-dimensional manifold and is diffeomorphic to the torus $T^2$.

b.Is there a complete $3$-dimensional Riemannian manifold $M$ and a point $p\in M$, such that the boundary of the open geodesic ball $B(p,r)$ for some $r>0$ is a smooth $2$-dimensional manifold and isisometricto the flat torus $T^2$? (The flat torus is defined as the direct product of two copies of $\mathbb{R}/\mathbb{Z}$)

Thanks for any help to the questions in advance.