Address:
School of Mathematical Sciences, University of Adelaide, SA 5005, Australia
Department of Mathematics and Statistics, Masaryk University, 611 37 Brno, Czech Republic
E-mail:
meastwoo@gmail.com
slovak@math.muni.cz
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.
AMSclassification: primary 53D05; secondary 53B35.
Keywords: symplectic structure, Kähler structure, tractor calculus, exact complex, BGG machinery.
DOI: 10.5817/AM2018-5-265