Communications in Analysis and Geometry

Volume 29 (2021)

Number 5

Manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type

Pages: 1233 – 1253

DOI:  https://dx.doi.org/10.4310/CAG.2021.v29.n5.a7

Authors

Huihong Jiang (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Yi-Hu Yang (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Abstract

We construct a complete $n$-dimensional $(n \geq 6)$ Riemannian manifold of positive Ricci curvature with quadratically asymptotically nonnegative sectional curvature and infinite topological type. This gives a negative answer to a problem proposed by Jiping Sha and Zhongmin Shen [12] in the case of $n \geq 6$.

The authors were partially supported by NSF of China (No.11571228).

Received 4 January 2018

Accepted 4 January 2019

Published 1 December 2021