The Dolbeault operator on Hermitian spin surfaces
| dc.creator | Alexandrov, Bogdan | |
| dc.creator | Grantcharov, Gueo | |
| dc.creator | Ivanov, Stefan | |
| dc.date | 1999-02-01 | |
| dc.date.accessioned | 2026-07-07T05:27:44Z | |
| dc.date.available | 2026-07-07T05:27:44Z | |
| dc.description | We consider the Dolbeault operator of $K^{1/2}$ -- the square root of the canonical line bundle which determines the spin structure of a compact Hermitian spin surface (M,g,J). We prove that the Dolbeault cohomology groups of $K^{1/2}$ vanish if the scalar curvature of g is non-negative and non-identically zero. Moreover, we estimate the first eigenvalue of the Dolbeault operator when the conformal scalar curvature k is non-negative and when k is positive. In the first case we give a complete list of limiting manifolds and in the second one we give non-Kähler examples of limiting manifolds. | |
| dc.description | 11 pages, Latex format, no figures | |
| dc.identifier | https://arxiv.org/abs/math/9902005 | |
| dc.identifier | http://arxiv.org/abs/math/9902005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78031 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C55, 53C15 | |
| dc.title | The Dolbeault operator on Hermitian spin surfaces | |
| dc.type | text |