Communications in Analysis and Geometry
Volume 29 (2021)
Manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type
Pages: 1233 – 1253
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  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