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

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.

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.

@article{AIF_1986__36_2_83_0,
     author = {Seaman, Walter},
     title = {The third {Betti} number of a positively pinched riemannian six manifold},
     journal = {Annales de l'Institut Fourier},
     pages = {83--92},
     year = {1986},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {36},
     number = {2},
     doi = {10.5802/aif.1049},
     zbl = {0578.53031},
     mrnumber = {87k:53096},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1049/}
}
TY  - JOUR
AU  - Seaman, Walter
TI  - The third Betti number of a positively pinched riemannian six manifold
JO  - Annales de l'Institut Fourier
PY  - 1986
SP  - 83
EP  - 92
VL  - 36
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1049/
DO  - 10.5802/aif.1049
LA  - en
ID  - AIF_1986__36_2_83_0
ER  - 
%0 Journal Article
%A Seaman, Walter
%T The third Betti number of a positively pinched riemannian six manifold
%J Annales de l'Institut Fourier
%D 1986
%P 83-92
%V 36
%N 2
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1049/
%R 10.5802/aif.1049
%G en
%F AIF_1986__36_2_83_0
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

[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. | Zbl | MR

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

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

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

[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. | Zbl | MR | Numdam

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

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

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

Cité par Sources :