2022/06/29 by Windare, Oluwagbenga Joshua
#14L24 #53D20 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2206.14725
We study the action of a real reductive group G on a Kahler manifold Z which is the restriction of a holomorphic action of a complex reductive Lie group U^ℂ. We assume that the action of U, a maximal compact connected subgroup of U^ℂ on Z is Hamiltonian. If G⊂ U^ℂ is compatible, there is a corresponding gradient map μ_\mathfrakp: Z→ \mathfrakp, where \mathfrakg = \mathfrakk ⊕ \mathfrakp is a Cartan decomposition of the Lie algebra of G. Our main results are the openness and connectedness of the set of semistable points associated with G-action on Z, a convexity theorem for the G-action on a G-invariant compact Lagrangian submanifold of Z, and a convexity result for two-orbit variety.