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
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