Almost Parity Structure, Connections and Vielbeins in BV Geometry
| dc.creator | Bering, K. | |
| dc.date | 1997-11-12 | |
| dc.date | 1998-02-06 | |
| dc.date.accessioned | 2026-07-07T10:15:53Z | |
| dc.date.available | 2026-07-07T10:15:53Z | |
| dc.description | We observe that an anti-symplectic manifold locally always admits a parity structure. The parity structure can be viewed as a complex-like structure on the manifold. This induces an odd metric and its Levi-Civita connection, and thereby a new notion of an odd Kaehler geometry. Oversimplified, just to capture the idea, the bosonic variables are ``holomorphic'', while the fermionic variables are ``anti-holomorphic''. We find that an odd Kaehler manifold in this new ``complex'' sense has a nilpotent odd Laplacian iff it is Ricci-form-flat. The local cohomology of the odd Laplacian is derived. An odd Calabi-Yau manifold has locally a canonical volume form. We suggest that an odd Calabi-Yau manifold is the natural geometric notion to appear in covariant BV-quantization. Finally, we give a vielbein formulation of anti-symplectic manifolds. | |
| dc.description | 36 pages, LaTeX, Several modifications. New definition of an ``odd Calabi-Yau'' manifold | |
| dc.identifier | https://arxiv.org/abs/physics/9711010 | |
| dc.identifier | http://arxiv.org/abs/physics/9711010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173326 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Differential Geometry | |
| dc.title | Almost Parity Structure, Connections and Vielbeins in BV Geometry | |
| dc.type | text |