Abstract

In analogous to flat bundle and holomorphic bundle, we introduce a special type of vector bundle over symplectic manifolds, which is called symplectically flat. The corresponding connection is called a symplectically flat connection and its curvature is proportional to the symplectic form. Considering that flat connections are the zero points of Yang-Mills functional, we construct two similar functionals vanishing on the symplectically flat connections, then study their critical points. This work is in joint with Li-Sheng Tseng.