The cohomology groups of a special Einstein manifold

Summary We consider a compact orientable Einstein manifold of even dimension n=2m, which is k-pinched. If k>m(m−1) ₂ (2m−1) ₂ (2m−1)+3], then there exists no element, different from zero of the H ₂ (M,R) such that its exterior m-power belongs to a zero class. This result has some applications to the topological product of manifold. Entrata in Redazione il 27 settembre 1977.