Hermitian Structures and Compatible Connections on A-bundles
| dc.creator | Papatriantafillou, Maria | |
| dc.date | 1998-10-15 | |
| dc.date.accessioned | 2026-07-07T05:26:28Z | |
| dc.date.available | 2026-07-07T05:26:28Z | |
| dc.description | A-manifolds and A-bundles are manifolds and vector bundles modelled on a projective finitely generated module over a topological algebra A. In this paper we investigate the conditions under which an A-bundle is provided with an A-valued hermitian structure and a compatible connection, in case A is a commutative complete locally m-convex C*-algebra with unit. In this investigation two obstacles appear: first, A-manifolds do not admit partitions of unity in the classical sence, and, secondly, the existence of a hermitian structure is not equivalent to the reduction of the structural group of the bundle to a certain subgroup. However, we prove that if the bundle has a trivializing covering whose transition functions take values in the group of the "A-hermitian product preserving" automorphisms of the fibre type and the base space admits at least one A-valued partition of unity (subordinate to this covering), then the A-bundle admits an A-hermitian structure and a compatible connection. | |
| dc.description | Latex, 12 pages, to be published in the Proc. 2nd Conf. of Balkan Soc of Geometers, Thessaloniki, 1998 | |
| dc.identifier | https://arxiv.org/abs/math/9810096 | |
| dc.identifier | http://arxiv.org/abs/math/9810096 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77562 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58B20 (Primary), 53C05 (Secondary) | |
| dc.title | Hermitian Structures and Compatible Connections on A-bundles | |
| dc.type | text |