Let (M, J, g, ω) be a complete Hermitian manifold of complex dimension n≥ 2. Let 1 ≤ p≤ n- 1 and assume that ωn-p is (∂+ ∂¯) -bounded. We prove that, if ψ is an L2 and d-closed (p, 0)-form on M, then ψ= 0. In particular, if M is compact, we derive that if the Aeppli class of ωn-p vanishes, then HBCp,0(M)=0. As a special case, if M admits a Gauduchon metric ω such that the Aeppli class of ωn-1 vanishes, then HBC1,0(M)=0.

Aeppli Cohomology and Gauduchon Metrics / Piovani, R.; Tomassini, A.. - In: COMPLEX ANALYSIS AND OPERATOR THEORY. - ISSN 1661-8254. - 14:1(2020). [10.1007/s11785-020-00984-6]

Aeppli Cohomology and Gauduchon Metrics

Piovani R.;Tomassini A.
2020

Abstract

Let (M, J, g, ω) be a complete Hermitian manifold of complex dimension n≥ 2. Let 1 ≤ p≤ n- 1 and assume that ωn-p is (∂+ ∂¯) -bounded. We prove that, if ψ is an L2 and d-closed (p, 0)-form on M, then ψ= 0. In particular, if M is compact, we derive that if the Aeppli class of ωn-p vanishes, then HBCp,0(M)=0. As a special case, if M admits a Gauduchon metric ω such that the Aeppli class of ωn-1 vanishes, then HBC1,0(M)=0.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2886539
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