A note on the reduction of Sasakian manifolds (Q2715737)

The first example of a reduction procedure for manifolds with some structure was presented by \textit{J. Marsden} and \textit{A. Weinstein} [Rep. Math. Phys. 5, 121-130 (1974; Zbl 0327.58005)] for manifolds with a symplectic structure. Later, \textit{H. Geiges} [Math. Proc. Camb. Philos. Soc. 121, 455-564 (1997; Zbl 0882.57007)] extended it to manifolds with a contact structure. In the present article, the authors show that Geiges' reduction technique also works in the Sasakian setting, i.e., for contact metric spaces with a compatible metric and satisfying a curvature condition. Passing to the Kähler cone over a Sasakian space, one can relate this reduction to the reduction of Kähler spaces. The authors illustrate the theory by an example of a \(SU(2)\) reduction of a standard Sasakian sphere \(S^{4n-1}\).NEWLINENEWLINEFor the entire collection see [Zbl 0958.00032].