Orthogonally pinched curvature tensors and applications. Walter Seaman — 1991 Mathematica Scandinavica
The third Betti number of a positively pinched riemannian six manifold Walter Seaman — 1986 Annales de l'institut Fourier We prove that if the sectional curvature, K , of a compact 6-manifold without boundary satisfies 1 ≥ K > ( 4 10 - 4 ) / ( 4 10 + 23 ) ≅ . 2426 , then its third (real) Betti number is zero.