4 F eb 1 99 9 Weyl structures with positive Ricci tensor
نویسنده
چکیده
We prove the vanishing of the first Betti number on compact manifolds admitting a Weyl structure whose Ricci tensor satisfies certain positivity condition. Thus we obtain a generalization of the vanishing theorem of Bochner, which has a particularly simple form in dimension 4. As a corollary we obtain that if the canonical Weyl structure on a compact Hermitian surface is non-exact, the symmetric part of its Ricci tensor is non-negative and the first Betti number is not zero, then with respect to the Gauduchon metric the surface is a generalized Hopf surface.
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