Some complex Grassmannian manifolds that do not fibre nontrivially (Q1187111)

A finite CW complex is said to be prime if it cannot be the total space of a Hurewicz fibration with compact non-contractible fibre and base. R. Schultz conjectured that homogeneous spaces with non-zero Euler- Poincaré numbers were prime if they satisfied a few other conditions. The author shows that Complex Grassmannians \(G_{n,3}\) for \(n=4k+3\) and \(k > 0\), is prime. Related results are proved for \(G_{3,n}\) and \(G_{n,4}\) for other classes of \(n\).