Calculus on symplectic manifolds

EASTWOOD, Michael George and Jan SLOVÁK. Calculus on symplectic manifolds. Archivum Mathematicum. Brno: Masarykova Universita, 2018, 54 (2018), No 5, p. 265-280. ISSN 1212-5059. Available from: https://dx.doi.org/10.5817/AM2018-5-265.

Basic information

• Original name: Calculus on symplectic manifolds
• Authors: EASTWOOD, Michael George (826 United Kingdom of Great Britain and Northern Ireland) and Jan SLOVÁK (203 Czech Republic, guarantor, belonging to the institution).
• Edition: Archivum Mathematicum, Brno, Masarykova Universita, 2018, 1212-5059.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10100 1.1 Mathematics
• Country of publisher: Czech Republic
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• RIV identification code: RIV/00216224:14310/18:00101831
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.5817/AM2018-5-265
• UT WoS: 000462184000003
• Keywords in English: symplectic structure;Kähler structure;tractor calculus;exact complex;BGG machinery
• Tags: rivok
• Tags: International impact, Reviewed

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.

Links

• GBP201/12/G028, research and development project: Name: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Investor: Czech Science Foundation