dc.contributor.author | Li, Xiaolong | |

dc.date.accessioned | 2023-01-09T16:59:40Z | |

dc.date.available | 2023-01-09T16:59:40Z | |

dc.date.issued | 2022-08-04 | |

dc.identifier.citation | Li, X. Manifolds with $4\frac{1}{2}$-Positive Curvature Operator of the Second Kind. J Geom Anal 32, 281 (2022). https://doi.org/10.1007/s12220-022-01033-8 | |

dc.identifier.issn | 1559-002X | |

dc.identifier.uri | https://doi.org/10.1007/s12220-022-01033-8 | |

dc.identifier.uri | https://soar.wichita.edu/handle/10057/24866 | |

dc.description | Click on the DOI to access this article (may not be free). | |

dc.description.abstract | We show that a closed four-manifold with $4\frac{1}{2}$-positive curvature operator of the second kind is diffeomorphic to a spherical space form. The curvature assumption is sharp as both ${\mathbb{CP}\mathbb{}}^2$and ${\mathbb {S}}^3 \times {\mathbb {S}}^1$have $4\frac{1}{2}$-nonnegative curvature operator of the second kind. In higher dimensions $n\ge 5$, we show that closed Riemannian manifolds with $4\frac{1}{2}$-positive curvature operator of the second kind are homeomorphic to spherical space forms. These results are proved by showing that $4\frac{1}{2}$-positive curvature operator of the second kind implies both positive isotropic curvature and positive Ricci curvature. Rigidity results for $4\frac{1}{2}$-nonnegative curvature operator of the second kind are also obtained. | |

dc.language.iso | en_US | |

dc.publisher | Springer Nature | |

dc.relation.ispartofseries | The Journal of Geometric Analysis | |

dc.relation.ispartofseries | Volume 32 | |

dc.subject | Curvature operator of the second kind | |

dc.subject | Nishikawa’s conjecture | |

dc.subject | Sphere theorem | |

dc.subject | Positive isotropic curvature | |

dc.title | Manifolds with $4\frac{1}{2}$-Positive Curvature Operator of the Second Kind | |

dc.type | Article | |

dc.rights.holder | © Mathematica Josephina, Inc. 2022 | |