Riemannian manifolds with entire Grauert tube are rationally elliptic

Chen, Xiaoyang

doi:10.2140/gt.2024.28.1099

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Riemannian manifolds with entire Grauert tube are rationally elliptic

Xiaoyang Chen

Geometry & Topology 28 (2024) 1099–1112

DOI: 10.2140/gt.2024.28.1099

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 $T M$ . 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

Open Access made possible by participating institutions via Subscribe to Open.

Volume 28, issue 3 (2024)