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PreprintCC0arXiv

Nonnegative curvature on vector bundles over CP3 and its blow-up

  • Wen Shen
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Abstract

Every real vector bundle of rank at least seven over CP3, or every real vector bundle of rank at least eight over CP3#CP3, 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 S4 and CP2.

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Cite

BibTeXRIS
BibTeX
@misc{shen2026nonnegative,
  title = {{Nonnegative curvature on vector bundles over $CP^3$ and its blow-up}},
  author = {Wen Shen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06659},
  eprint = {2609.06659},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06659},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Nonnegative curvature on vector bundles over CP^3 and its blow-up
AU  - Wen Shen
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06659
UR  - https://arxiv.org/abs/2609.06659
AB  - 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.
ER  -