$CP^3$ 及其 blow-up 上向量丛的非负曲率
Nonnegative curvature on vector bundles over ${CP}^3$ and its blow-up
- College of Mathematics and Physics, Wenzhou University（温州大学数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明 $CP^3$ 上秩至少七、$CP^3\#CP^3$ 上秩至少八的实向量丛及其单位球面丛具有非负截面曲率的完备度量，通过低维丛分类与 Grove--Ziller 提升理论实现。
AI中文摘要：
秩至少为七的实向量丛在 $CP^3$ 上，或秩至少为八的实向量丛在 $CP^3\#CP^3$ 上，其全空间均容许一个具有非负截面曲率的完备度量。相应的单位球面丛也容许非负截面曲率。这些是固定秩的结果：不需要额外的平凡直和项，且对任何示性类没有限制。证明结合了低维丛分类与在 $S^4$ 和 $CP^2$ 上的 Grove--Ziller 提升理论。
英文摘要：
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 $CP^2$.
