Non-negative curvature on the product manifold of 7-sphere and homotopy ℂℙ³
Abstract
Let h C P 3 \mathrm {h}\mathbb {CP}^3 denote a 6 6 -dimensional smooth manifold that is homotopy equivalent to the complex 3 3 -dimensional projective space C P 3 \mathbb {CP}^3 . In this paper, we prove that if the first Pontrjagin class of h C P 3 \mathrm {h}\mathbb {CP}^3 satisfies p 1 ( h C P 3 ) ≥ 4 \mathfrak p_1(\mathrm {h}\mathbb {CP}^3)\geq 4 , then the product manifold h C P 3 × S 7 \mathrm {h}\mathbb {CP}^3\times S^7 admits a Riemannian metric with non-negative sectional curvature. This conclusion follows from the diffeomorphism property: h C P 3 × S 7 \mathrm {h}\mathbb {CP}^3\times S^7 is diffeomorphic to a certain manifold which admits a Riemannian metric with non-negative sectional curvature.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 3
- Pages
- 1261–1268
- Publication date
- 15 January 2026
- Language
- EN