Abstract:  Given a projective map F:M→N of a complete Riemannian manifold to a Riemannian  manifold with the sectional curvature bounded above by a negative constant,we prove that f de- creases volume up to a constant depending only on the curvatures of M and N.This generalizes the result due to Har'el.

Key words:  , projective , map, volume-decreasing, Ricci , curvature, sectional , curvature