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FOUR-MANIFOLDS WITH POSITIVE CURVATURE
Published online by Cambridge University Press: 06 April 2020
Abstract
In this note, we prove that a four-dimensional compact oriented half-conformally flat Riemannian manifold M4 is topologically
$\mathbb{S}^{4}$
or
$\mathbb{C}\mathbb{P}^{2}$
, provided that the sectional curvatures all lie in the interval
$\left[ {{{3\sqrt {3 - 5} } \over 4}, 1} \right]$
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.
- Type
- Research Article
- Information
- Copyright
- © Glasgow Mathematical Journal Trust 2020
Footnotes
E. Ribeiro Jr. was partially supported by grants from CNPq/Brazil (Grant: 303091/2015-0), PRONEX-FUNCAP/CNPq/Brazil, and CAPES/Brazil – Finance Code 001.
E. Rufino was partially supported by CAPES/Brazil.
References
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