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- W4283756688 abstract "We show that compact, $n$-dimensional Riemannian manifolds with $frac{n+2}{2}$-nonnegative curvature operators of the second kind are either rational homology spheres or flat. More generally, we obtain vanishing of the $p$-th Betti number provided that the curvature operator of the second kind is $C(p,n)$-positive. Our curvature conditions become weaker as $p$ increases. For $p=frac{n}{2}$ we have $C(p,n)= frac{3n}{2} frac{n+2}{n+4} $, and for $5 leq p leq frac{n}{2}$ we exhibit a $C(p,n)$-positive algebraic curvature operator of the second kind with negative Ricci curvatures." @default.
- W4283756688 created "2022-07-02" @default.
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- W4283756688 date "2022-06-28" @default.
- W4283756688 modified "2023-09-26" @default.
- W4283756688 title "Betti numbers and the curvature operator of the second kind" @default.
- W4283756688 doi "https://doi.org/10.48550/arxiv.2206.14218" @default.
- W4283756688 hasPublicationYear "2022" @default.
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