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arXiv · 1406.0327

The topology of closed manifolds with quasi-constant sectional curvature

Louis Funar
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Abstract

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable positivity assumption and for torsion-free fundamental groups they are still diffeomorphic to connected sums of spherical space forms and spherical bundles over the circle.

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Louis Funar. 2014-06-02. The topology of closed manifolds with quasi-constant sectional curvature. https://arxiv.org/abs/1406.0327

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