Calculus on symplectic manifolds

Michael Eastwood; Jan Slovák

Archivum Mathematicum (2018)

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

Abstract

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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.

How to cite

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Eastwood, 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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