Kähler and Sasakian-Einstein Quotients

Details Kähler and Sasakian-Einstein Quotients Kähler and Sasakian-Einstein Quotients

2008-03-17

arxiv.org/abs/0803.2301v1

Mathematics

Differential Geometry

31 pages, 1 figure

Scientific paper

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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