Vanishing theorems on Hermitian manifolds

dc.creatorAlexandrov, Bogdan
dc.creatorIvanov, Stefan
dc.date1999-01-21
dc.date2003-01-09
dc.date.accessioned2026-07-07T05:27:36Z
dc.date.available2026-07-07T05:27:36Z
dc.descriptionWe prove the vanishing of the Dolbeault cohomology groups on Hermitian manifolds with $dd^c$-harmonic Kähler form and positive (1,1)-part of the Ricci form of the Bismut connection. This implies the vanishing of the Dolbeault cohomology groups on complex surfaces which admit a conformal class of Hermitian metrics, such that the Ricci tensor of the canonical Weyl structure is positive. As a corollary we obtain that any such surface must be rational with $c_1^2 >0$. As an application, the pth Dolbeault cohomology groups of a left-invariant complex structure compatible with a bi-invariant metric on a compact even dimensional Lie group are computed.
dc.description15 pages, Latex format, no figures; Added section
dc.identifierhttps://arxiv.org/abs/math/9901090
dc.identifierhttp://arxiv.org/abs/math/9901090
dc.identifierDiffer. Geom. Appl. 14, No.3, 251-265 (2001)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77982
dc.subjectDifferential Geometry
dc.subject53C55, 53C15
dc.titleVanishing theorems on Hermitian manifolds
dc.typetext

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