Riemannian manifolds with entire Grauert tube are rationally elliptic

Chen, Xiaoyang ¹

¹ School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Institute for Advanced Study, Tongji University, Shanghai, China

Geometry & topology, Tome 28 (2024) no. 3, pp. 1099-1112

Résumé

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.

Détail

DOI : 10.2140/gt.2024.28.1099

Keywords: entire Grauert tube, rationally ellipticity, nonnegative curvature

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