2016/12/12 by Graziano Gentili, Gentili, Graziano, Anna Gori +3 · 3 citations
Mathematics · #30G35 #52B20 #53D20 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.CV #math.DG #math.SG #msc:30G35 #msc:52B20 #msc:53D20
paper · pdf · doi:10.48550/arxiv.1612.03600
23 pages
arxiv created 2016/12/12 · arxiv updated 2016/12/19
In the present paper we introduce and study a new notion of toric manifold in the quaternionic setting. We develop a construction with which, starting from appropriate m-dimensional Delzant polytopes, we obtain manifolds of real dimension 4m, acted on by m copies of the group \rm Sp(1) of unit quaternions. These manifolds are quaternionic regular and can be endowed with a 4-plectic structure and a generalized moment map. Convexity properties of the image of the moment map are studied. Quaternionic toric manifolds appear to be a large enough class of examples where one can test and study new results in quaternionic geometry.