On the fundamental groups of positively curved 5-manifolds with maximal local symmetry rank

• Autores: Jin Hong Kim, Hee Kwon Lee
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 37, Nº 3, 2011, págs. 787-792
• Idioma: inglés
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• Resumen

  • Let M be a closed oriented Riemannian manifold of dimension 5 with positive sectional curvature. If M admits an effective and isometric torus action of rank 2 or 3 which is invariant under the fundamental group of M, 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 an effective and isometric torus action of rank 3 which is invariant under the fundamental group of M, then its fundamental group is actually cyclic. Furthermore, we show that if the fundamental group of M is not isomorphic to the cyclic group of order 3 as well, then M is diffeomorphic to a lens space.