Geodesic
Calculus on symplectic manifolds
Archivum mathematicum, Tome 54 (2018) no. 5, pp. 265-280

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.5817/AM2018-5-265
Classification : 53B35, 53D05
Keywords: symplectic structure; Kähler structure; tractor calculus; exact complex; BGG machinery 
@article{10_5817_AM2018_5_265,
     author = {Eastwood, Michael and Slov\'ak, Jan},
     title = {Calculus on symplectic manifolds},
     journal = {Archivum mathematicum},
     pages = {265--280},
     publisher = {mathdoc},
     volume = {54},
     number = {5},
     year = {2018},
     doi = {10.5817/AM2018-5-265},
     mrnumber = {3887354},
     zbl = {06997355},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2018-5-265/}
}
TY  - JOUR
AU  - Eastwood, Michael
AU  - Slovák, Jan
TI  - Calculus on symplectic manifolds
JO  - Archivum mathematicum
PY  - 2018
SP  - 265
EP  - 280
VL  - 54
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2018-5-265/
DO  - 10.5817/AM2018-5-265
LA  - en
ID  - 10_5817_AM2018_5_265
ER  - 
%0 Journal Article
%A Eastwood, Michael
%A Slovák, Jan
%T Calculus on symplectic manifolds
%J Archivum mathematicum
%D 2018
%P 265-280
%V 54
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2018-5-265/
%R 10.5817/AM2018-5-265
%G en
%F 10_5817_AM2018_5_265
Eastwood, Michael; Slovák, Jan. Calculus on symplectic manifolds. Archivum mathematicum, Tome 54 (2018) no. 5, pp. 265-280. doi: 10.5817/AM2018-5-265

Cité par Sources :