ON THE FUNDAMENTAL GROUPS OF POSITIVELY CURVED 5-MANIFOLDS WITH MAXIMAL LOCAL SYMMETRY RANK

Abstract

Let M be a closed oriented Riemannian manifold of dimension 5 with positive sectional curvature. If M admits a pi(1)-invariant isometric T(k)-action (k = 2, 3), it has been shown by Fang and Rong that M is homeomorphic to a spherical space form. In this paper, we show that if M admits a pi(1)-invariant isometric T(3)-action, then pi(1)(M) is actually cyclic. Furthermore, we show that if pi(1)(M) is not isomorphic to Z(3) as well, then M is diffeomorphic to a lens space.