Four-manifolds with positive curvature

R. Diógenes; E. Ribeiro Jr.; E. Rufino

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arXiv · 1809.06150

Four-manifolds with positive curvature

R. Diógenes·E. Ribeiro Jr.·E. Rufino

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Abstract

In this note we prove that a four-dimensional compact oriented half-confor\-mally flat Riemannian manifold $M^4$ is topologically $\mathbb{S}^{4}$ or $\mathbb{C}\mathbb{P}^{2},$ provided that the sectional curvatures all lie in the interval $[\frac{3\sqrt{3}-5}{4},\,1].$ In addition, we use the notion of biorthogonal (sectional) curvature to obtain a pinching condition which guarantees that a four-dimensional compact manifold is homeomorphic to a connected sum of copies of the complex projective plane or the $4$-sphere.

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BibTeX RIS

R. Diógenes, E. Ribeiro Jr., E. Rufino. 2018-09-17. Four-manifolds with positive curvature. https://arxiv.org/abs/1809.06150

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