Sharp Bochner-type estimates show that sectional-scalar curvature pinching forces vanishing of the second Betti number, with the equality case forcing a complex projective space.
Diffeomorphism Finite- ness, Positive Pinching, and Second Homotopy
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Sharp Weitzenb\"{o}ck and PIC2 Estimates from Sectional-Scalar Curvature Pinching
Sharp Bochner-type estimates show that sectional-scalar curvature pinching forces vanishing of the second Betti number, with the equality case forcing a complex projective space.