JournalscmhVol. 74 , No. 3DOI 10.1007/s000140050097

Riemannian submersions of open manifolds which are flat at infinity

  • V. Marenich

    IMECC - UNICAMP, Campinas, Brazil
Riemannian submersions of open manifolds which are flat at infinity cover

Abstract

We prove that a base BnkB^{n-k} of a Riemannian submersion π:MnBnk\pi : {M^n} \to B^{n-k} is flat, if MnM^n is flat at infinity and BnkB^{n-k} is compact. As a corollary we obtain a topological gap-phenomenon for open manifolds of nonnegative sectional curvature (Eschenburg-Schroeder-Strake conjecture).