On foliations with Morse singularities

Abstract

We study codimension one smooth foliations with Morse type singularities on closed manifolds. We obtain a description of the manifold if there are more centers than saddles. This result relies on and extends previous results of Reeb for foliations having only centers, results of Wagneur for foliations with Morse singularities and results of Eells and Kuiper for manifolds admitting Morse functions with three singularities.