Complex contact manifolds and circle actions
Haydee Herrera, Rafael Herrera
TL;DR
This paper proves rigidity and vanishing theorems for holomorphic Euler characteristics on complex contact manifolds with circle symmetries, extending known results under curvature conditions to symmetry assumptions.
Contribution
It introduces new vanishing theorems for complex contact manifolds with circle actions, broadening the understanding of their geometric and topological properties.
Findings
Vanishing theorems for holomorphic Euler characteristics
Rigidity results under circle symmetry
Extension of LeBrun and Salamon's results
Abstract
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.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology