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Riemannian manifolds with entire Grauert tube are rationally elliptic

Xiaoyang Chen

Geometry & Topology 28 (2024) 1099–1112
Abstract

It was conjectured by Bott, Grove and 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, ie M is a real-analytic Riemannian manifold that has a unique adapted complex structure defined on the whole tangent bundle TM. Our result also provides a strong topological obstruction to the existence of an entire Grauert tube.

Keywords
entire Grauert tube, rationally ellipticity, nonnegative curvature
Mathematical Subject Classification
Primary: 53C20
References
Publication
Received: 3 January 2021
Revised: 5 May 2022
Accepted: 10 August 2022
Published: 10 May 2024
Proposed: Gang Tian
Seconded: John Lott, Dmitri Burago
Authors
Xiaoyang Chen
School of Mathematical Sciences
Key Laboratory of Intelligent Computing and Applications (Ministry of Education)
Institute for Advanced Study
Tongji University
Shanghai
China

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