JournalscmhVol. 74, No. 3pp. 419–441

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
Download PDF

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).

Cite this article

V. Marenich, Riemannian submersions of open manifolds which are flat at infinity. Comment. Math. Helv. 74 (1999), no. 3, pp. 419–441

DOI 10.1007/S000140050097