Analytic fields on compact balanced Hermitian manifolds
| dc.creator | Ganchev, George | |
| dc.creator | Ivanov, Stefan | |
| dc.date | 1996-06-24 | |
| dc.date.accessioned | 2026-07-07T09:12:48Z | |
| dc.date.available | 2026-07-07T09:12:48Z | |
| dc.description | On a Hermitian manifold we construct a symmetric $(1,1)$- tensor $H$ using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and sufficient conditions in terms of the tensor $H$ for a harmonic $1$-form to be analytic and for an analytic $1$-form to be harmonic. We prove that if $H$ is positive definite then the first Betti number $b_1 = 0$ and the Hodge number $h^{1,0} = 0$. We obtain an obstruction to the existence of Killing vector fields in terms of the Ricci tensor of the Chern connection: if the Chern form of the Chern connection on a compact balanced Hermitian manifold is non- positive definite then every Killing vector field is analytic; if moreover the Chern form is negative definite then there are no Killing vector fields. It is proved that on a compact balanced Hermitian manifold every affine with respect to the Chern connection vector field is an analytic vector field. | |
| dc.description | 14 pages, Latex format, no figures | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9606011 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9606011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152144 | |
| dc.subject | Differential Geometry | |
| dc.title | Analytic fields on compact balanced Hermitian manifolds | |
| dc.type | text |