Vanishing theorems on Hermitian manifolds
| dc.creator | Alexandrov, Bogdan | |
| dc.creator | Ivanov, Stefan | |
| dc.date | 1999-01-21 | |
| dc.date | 2003-01-09 | |
| dc.date.accessioned | 2026-07-07T05:27:36Z | |
| dc.date.available | 2026-07-07T05:27:36Z | |
| dc.description | We 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.description | 15 pages, Latex format, no figures; Added section | |
| dc.identifier | https://arxiv.org/abs/math/9901090 | |
| dc.identifier | http://arxiv.org/abs/math/9901090 | |
| dc.identifier | Differ. Geom. Appl. 14, No.3, 251-265 (2001) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77982 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C55, 53C15 | |
| dc.title | Vanishing theorems on Hermitian manifolds | |
| dc.type | text |