# Calculus on symplectic manifolds

Archivum Mathematicum (2018)

- Volume: 054, Issue: 5, page 265-280
- ISSN: 0044-8753

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topEastwood, Michael, and Slovák, Jan. "Calculus on symplectic manifolds." Archivum Mathematicum 054.5 (2018): 265-280. <http://eudml.org/doc/294700>.

@article{Eastwood2018,

abstract = {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.},

author = {Eastwood, Michael, Slovák, Jan},

journal = {Archivum Mathematicum},

keywords = {symplectic structure; Kähler structure; tractor calculus; exact complex; BGG machinery},

language = {eng},

number = {5},

pages = {265-280},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Calculus on symplectic manifolds},

url = {http://eudml.org/doc/294700},

volume = {054},

year = {2018},

}

TY - JOUR

AU - Eastwood, Michael

AU - Slovák, Jan

TI - Calculus on symplectic manifolds

JO - Archivum Mathematicum

PY - 2018

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 054

IS - 5

SP - 265

EP - 280

AB - 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.

LA - eng

KW - symplectic structure; Kähler structure; tractor calculus; exact complex; BGG machinery

UR - http://eudml.org/doc/294700

ER -

## References

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