2017/09/10 by Eastwood, Michael, Slovak, Jan
#53B35 #53D05 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1709.03059
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.