Year: 2026
Type: preprint
Abstract: Every real vector bundle of rank at least seven over $CP^3$, or every real vector bundle of rank at least eight over $CP^3\#CP^3$, admits a complete metric of nonnegative sectional curvature on its total space. The corresponding unit sphere bundles also admit nonnegative sectional curvature. These are fixed-rank results: no additional trivial summand is required, and there is no restriction on any characteristic class. The proof combines low-dimensional bundle classification with the Grove--Ziller lifting theory over $S^4$ and $CP^2$.
Source: arXiv (Cornell University)
Author: Shen, Wen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212009931