no. 2
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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     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},
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     year = {1986},
     doi = {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. https://aif.centre-mersenne.org/articles/10.5802/aif.1049/

[1] S. Aloff and N. R. Wallach, An Infinite Family of Distinct 7-Manifolds Admitting Positively Curved Riemannian Metrics, Bull. A.M.S., 81 (1975), 93-97. | MR | Zbl

[2] M. Berger, Sur quelques variétés riemanniennes suffisamment pincées, Bull. Soc. Math. Fr., 88 (1960), 57-71. | Numdam | MR | Zbl

[3] M. Berger, Sur les variétés riemanniennes pincées just au-dessous de 1/4, Ann. Inst. Fourier, Grenoble, 33-2 (1983), 135-150. | Numdam | MR | Zbl

[4] J. Dadok and R. Harvey, Calibrations on R6, Duke Math. J., 50 (1983), 1231-1243. | MR | Zbl

[5] S. Goldberg, Curvature and Homology, Dover Publications, 1962, 1982. | Zbl

[6] D. Hulin, Le second nombre de Betti d'une variété riemannienne (1/4 - ε) - pincée de dimension 4, Ann. Inst. Fourier, Grenoble, 33-2 (1983), 167-182. | Numdam | MR | Zbl

[7] F. Morgan, The Exterior Algebra ΛkRn and Area Minimization, Linear Algebra and its Applications, 66 (1985), 1-28. | MR | Zbl

[8] W. Poor, Differential Geometric Structures, McGraw Hill Book Co., 1981. | MR | Zbl

[9] N. R. Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. Math., 96 (1972), 277-295. | MR | Zbl

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