We prove that a base of a Riemannian submersion is flat, if is flat at infinity and is compact. As a corollary we obtain a topological gap-phenomenon for open manifolds of nonnegative sectional curvature (Eschenburg-Schroeder-Strake conjecture).
Cite this article
V. Marenich, Riemannian submersions of open manifolds which are flat at infinity. Comment. Math. Helv. 74 (1999), no. 3, pp. 419–441DOI 10.1007/S000140050097