Calculus on symplectic manifolds
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Archivum Mathematicum |
| MU Faculty or unit | |
| Citation | |
| Web | https://dml.cz/bitstream/handle/10338.dmlcz/147504/ArchMathRetro_054-2018-5_3.pdf |
| Doi | http://dx.doi.org/10.5817/AM2018-5-265 |
| Keywords | symplectic structure;Kähler structure;tractor calculus;exact complex;BGG machinery |
| Description | On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic form, we find a new complex. In particular, on complex projective space with its Fubini–Study form and connection, we can build a series of differential complexes akin to the Bernstein–Gelfand–Gelfand complexes from parabolic differential geometry. |
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