A note on the fundamental group of a compact minimal hypersurface

Gregory James Galloway

Vol. 126 (1987), No. 2, 243–251

DOI: 10.2140/pjm.1987.126.243

Abstract

In this paper we generalize a well-known result of Frankel which relates the fundamental group of a complete Riemannian manifold with positive Ricci curvature to the fundamental group of a compact immersed minimal hypersurface. Here we consider the situation in which the Ricci curvature of the ambient manifold is only assumed to be nonnegative, and show that the conclusion of Frankel’s theorem can fail only under special circumstances.

Mathematical Subject Classification 2000

Primary: 53C42

Secondary: 53C20

Milestones

Received: 3 June 1985

Revised: 26 December 1985

Published: 1 February 1987