  A singular Riemannian foliation $F$ on a complete Riemannian manifold $M$ is
called a polar foliation if, for each regular point $p$, there is an immersed
submanifold $\Sigma$, called section, that passes through $p$ and that meets
all the leaves and always perpendicularly. A typical example of a polar
foliation is the partition of $M$ into the orbits of a polar action, i.e., an
isometric action with sections. In this work we prove that the leaves of $F$
coincide with the level sets of a smooth map $H: M\to \Sigma$ if $M$ is simply
connected. In particular, we have that the orbits of a polar action on a simply
connected space are level sets of an isoparametric map. This result extends
previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter
and West, and Terng.
