  The purpose of this paper is to prove the following theorem. Let $X$ be a
projective normal variety defined over an algebraically closed field of
characteristic zero and let $\Omega_{X}^{1}\to L$ be a one-dimensional
foliation on $X$. If $L\cdot C<0$ for all curves $C\subset X$ then either the
foliation is regular or else $X$ is a cone over a normal projective variety.
This strengthens Wahl's well-known cohomological characterization of the
projective space and gives a geometric proof of his results.
