Homogeneous Kähler structures on principal R^×-bundles reduce to Sasakian structures exactly when the Euler vector field is pre-geodesic and the line bundle is oriented, and the same dictionary covers co-Kähler structures as the 'invariant' case.
Normal Forms for Dirac-Jacobi bundles and Splitting Theorems for Jacobi Structures
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abstract
The aim of this paper is to prove a normal form Theorem for Dirac-Jacobi bundles using the recent techniques from Bursztyn, Lima and Meinrenken. As the most important consequence, we can prove the splitting theorems of Jacobi pairs which was proposed by Dazord, Lichnerowicz and Marle. As an application we provide a alternative proof of the splitting theorem of homogeneous Poisson structures.
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On Homogeneous K\"ahler Manifolds
Homogeneous Kähler structures on principal R^×-bundles reduce to Sasakian structures exactly when the Euler vector field is pre-geodesic and the line bundle is oriented, and the same dictionary covers co-Kähler structures as the 'invariant' case.