We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Circle action
- Complex contact manifold
- Holomorphic Euler characteristic