The third Betti number of a positively pinched riemannian six manifold
Annales de l'Institut Fourier, Tome 36 (1986) no. 2, pp. 83-92.

Nous démontrons que si la courbure sectionnelle K d’une variété riemannienne compacte de dimension 6 satisfait à la condition 1≥K>(410-4)/(410+23)≅.2426, alors son troisième (réel) nombre de Betti est nul.

We prove that if the sectional curvature, K, of a compact 6-manifold without boundary satisfies 1≥K>(410-4)/(410+23)≅.2426, then its third (real) Betti number is zero.

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     author = {Seaman, Walter},
     title = {The third {Betti} number of a positively pinched riemannian six manifold},
     journal = {Annales de l'Institut Fourier},
     pages = {83--92},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {36},
     number = {2},
     year = {1986},
     doi = {10.5802/aif.1049},
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     zbl = {0578.53031},
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     url = {http://www.numdam.org/articles/10.5802/aif.1049/}
}
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Seaman, Walter. The third Betti number of a positively pinched riemannian six manifold. Annales de l'Institut Fourier, Tome 36 (1986) no. 2, pp. 83-92. doi : 10.5802/aif.1049. http://www.numdam.org/articles/10.5802/aif.1049/

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