On the classification of certain 1-connected 7-manifolds and related problems

Abstract

In this article, we give a classification of closed, smooth, spin, 1-connected 7-manifolds whose integral cohomology ring is isomorphic to that of $\mathbb{C}P^2\times S^3$. We also prove that if a closed, smooth, spin, 1-connected 7-manifold has integral cohomology ring isomorphic to that of $\mathbb{C}P^2\times S^3$ or $S^2\times S^5$, then it admits a Riemannian metric with positive Ricci curvature.Comment: 20 page