K\"ahler and Sasakian-Einstein Quotients
Oana Mihaela Dr\u{a}gulete
TL;DR
This paper develops a framework for symplectic and K"ahler ray reduction, exploring their properties, relations with existing constructions, and applications to Einstein manifolds and Hamiltonian systems.
Contribution
It introduces a well-defined K"ahler reduction for non-isotropic momentum values and analyzes its compatibility with cone and Boothby-Wang constructions.
Findings
Ray quotients of cotangent bundles are explicitly described.
Conditions for quotients of Einstein manifolds to remain Einstein are provided.
Applications to conformal Hamiltonian systems are discussed.
Abstract
We construct symplectic and K\"ahler ray reduced spaces and discuss their relation with the Marsden-Weinstein (point) reduction. This K\"ahler reduction is well defined even when the momentum value is not totally isotropic. The compatibility of the ray reduction with the cone construction and the Boothby-Wang fibration is presented. Using the compatibility with the cone construction we provide the exact description of ray quotients of cotangent bundles. Some applications of the ray reduction to the study of conformal Hamiltonian systems are described. We also give necessary and sufficient conditions for the (ray) quotients of K\"ahler (Sasakian)-Einstein manifolds to be again K\"ahler (Sasakian)-Einstein.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Algebra and Geometry