Geodesic
Calculus on symplectic manifolds
Archivum mathematicum, Tome 54 (2018) no. 5, pp. 265-280 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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 
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Eastwood, Michael; Slovák, Jan. Calculus on symplectic manifolds. Archivum mathematicum, Tome 54 (2018) no. 5, pp. 265-280. doi: 10.5817/AM2018-5-265

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