Parole chiave

• sectional curvature
• Ricci curvature
• Riemannian manifold

Abstract I will present joint work with Miguel Domínguez Vázquez, David González-Álvaro, and Jason DeVito, focused on constructing the first examples of compact Riemannian manifolds with $\text{Ric}_2>0$ curvature in dimensions 10, 11, 12, 13, and 14. The condition $\text{Ric}_2 > 0$ is an intermediate curvature condition that interpolates between positive sectional curvature ($\text{sec} > 0$) and positive Ricci curvature ($\text{Ric} > 0$). We achieve this using a generalization of the fat bundle notion.