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math.DG2026
Sectional Curvature, Isotropic Curvature, and Yau's Pinching Problem
Xiaolong Li
We prove that if a closed Riemannian manifold has finite fundamental group and satisfies the curvature condition \begin{equation*} R_{1313} +R_{1414} +R_{2323} + R_{2424}…
math.DG2025
New Sphere Theorems under Curvature Operator of the Second Kind
Xiaolong Li
We investigate Riemannian manifolds whose curvature operator of the second kind satisfies the condition \begin{equation*} α^{-1} (λ_1 +\cdots +λ_α) > -…