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arXiv · 2101.04368

Riemannian manifolds with entire Grauert tube are rationally elliptic

Xiaoyang Chen
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Abstract

It was conjectured by Bott-Grove-Halperin that a compact simply connected Riemannian manifold $M$ with nonnegative sectional curvature is rationally elliptic. We confirm this conjecture under the stronger assumption that $M$ has entire Grauert tube,i.e.,$M$ is a real analytic Riemannian manifold that has a unique adapted complex structure defined on the whole tangent bundle $TM$.

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Xiaoyang Chen. 2021-01-12. Riemannian manifolds with entire Grauert tube are rationally elliptic. https://arxiv.org/abs/2101.04368

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