## Abstract

S.-S. Chern raised the question of determining those compact 3-manifolds M admitting a contact metric structure whose characteristic vector field generates a one-parameter group of isometries. S. Tachibana showed that the first betti number of these spaces must be even, and H. Sato proved that the second homotopy group of M is zero unless M is homotopy equivalent to S^{1}×S^{2}. A. Weinstein pointed out that M is a Seifert fibre space over an orientable surface. In this paper, it is shown as a consequence of a more general theorem that if, in addition, the scalar curvature is suitably bounded below by a negative constant, then the metric may be deformed to a metric of positive constant sectional curvature. Thus, if the manifold is simply connected it is diffeomorphic with the 3-sphere.

Original language | English (US) |
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Pages (from-to) | 365-372 |

Number of pages | 8 |

Journal | Tohoku Mathematical Journal |

Volume | 39 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1987 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Contact Riemannian manifolds
- Curvature
- Torsion