Summary
We consider a compact orientable Biemannian manifold M of dimension n=2m+1. We suppose that the manifold is positively k-pinched. In the present paper we have proved that if k>λ=2(2m−1)(m−1)2m/[m(m−1)(2m−3)(8m−5)+3], then the second Betti number of the manifold is zero. This number λ is an improvement than the number given in ([1]).
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Entrata in Redazione il 4 marzo 1969.
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Tsagas, G. An improvement of the method of Lichnerowicz-Bochner on the Betti numbers and curvature of a compact manifold. Annali di Matematica 83, 227–234 (1969). https://doi.org/10.1007/BF02411169
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DOI: https://doi.org/10.1007/BF02411169