Let (M, J, g,ω) be a Hermitian manifold of complex dimension n. Assume that the torsion of the Chern connection Δ is bounded, and that there exists a C∞exhausting function ρ : M → R such that Δρ,Δ2ρ are bounded. We characterize W1,2 Bott-Chern harmonic forms, extending the usual result that holds on compact Hermitian manifolds. Finally, if (M,J, g,ω) is Kähler complete, ω = dη, with η bounded, and the sectional curvature is bounded, then we get a vanishing theorem for W1,2 Bott-Chern harmonic (p, q)-forms, if p + q ≠= n.
Bott-Chern harmonic forms on complete Hermitian manifolds / Piovani, R.; Tomassini, A.. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 30:5(2019), p. 1950028. [10.1142/S0129167X19500289]
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