A Metric with Positive Sectional Curvature on $S^2\times S^3$

Shengtao Guo, Ethan X. Fang, Junwei Lu

We prove that $S^2\times S^3$ admits a Riemannian metric with positive sectional curvature. We regard it as the principal $S^1$-bundle with first Chern class $(1,1)$ over $S^2\time…