Construction of Ricci-type connections by reduction and induction
| dc.creator | Cahen, Michel | |
| dc.creator | Gutt, Simone | |
| dc.creator | Schwachhoefer, Lorenz | |
| dc.date | 2003-10-23 | |
| dc.date.accessioned | 2026-07-07T05:02:12Z | |
| dc.date.available | 2026-07-07T05:02:12Z | |
| dc.description | Given the Euclidean space $\R^{2n+2}$ endowed with a constant symplectic structure and the standard flat connection, and given a polynomial of degree 2 on that space, Baguis and Cahen have defined a reduction procedure which yields a symplectic manifold endowed with a Ricci-type connection. We observe that any symplectic manifold of dimension greater than 2 endowed with a symplectic connection of Ricci-type is locally given by a local version of such a reduction. We also consider the reverse of this reduction procedure, an induction procedure: we construct globally on a symplectic manifold endowed with a connection of Ricci-type $(M,ω,\nabla)$ a circle or a line bundle which embeds in a flat symplectic manifold $(P,μ,\nabla^1)$ as the zero set of a function whose third covariant derivative vanishes, in such a way that $(M,ω,\nabla)$ is obtained by reduction from $(P,μ,\nabla^1)$. We further develop the particular case of symmetric symplectic manifolds with Ricci-type connections. | |
| dc.identifier | https://arxiv.org/abs/math/0310375 | |
| dc.identifier | http://arxiv.org/abs/math/0310375 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68965 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.title | Construction of Ricci-type connections by reduction and induction | |
| dc.type | text |