5-DIMENSIONAL CONTACT MANIFOLDS WITH SECOND BETTI NUMBER {b_2} = 0
1989 年 41 巻 1 号 p. 163-170
詳細
1989 年 41 巻 1 号 p. 163-170
In this paper we improve some results of S.I. Goldberg ([3], [4]) in the 5-dimensional case. As consequences we obtain:
(a) the sphere {S^5} is the only compact simply connected normal homogeneous contact manifold of dimension 5 with {b_2} = 0;
(b) if a 5-dimensional compact simply connected regular Sasakian manifold is μ -holomorphically pinched with μ >1/2, then it is homeomorphic with a sphere.
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