Publication details

Calculus on symplectic manifolds

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EASTWOOD Michael George SLOVÁK Jan

Year of publication 2018
Type Article in Periodical
Magazine / Source Archivum Mathematicum
MU Faculty or unit

Faculty of Science

Keywords symplectic structure;Kähler structure;tractor calculus;exact complex;BGG machinery
Description 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.
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