The multi-moment map of the nearly Kähler S³ × S³

2017/02/17 by Kael Dixon, Dixon, Kael
Mathematics · #53C55 53D20 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C55 #msc:53D20

paper · pdf · doi:10.48550/arxiv.1702.05297

9 pages, 1 figure

arxiv created 2017/02/17 · openalex publication_date 2017/02/17 · arxiv updated 2017/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the multi-moment map associated to an almost Hermitian manifold which admits an action of a torus by holomorphic isometries. We investigate in particular the case of a \mathbb T³ action on the homogeneous nearly Kähler S³× S³. We find that the multi-moment map in this case acts more-or-less similarly to the moment map of a toric manifold, while the more general case does not.

Related

• Multi-moment maps on nearly Kähler six-manifolds
• Global properties of toric nearly Kähler manifolds
• Hypertoric manifolds and hyperKähler moment maps
• Moment maps and non-compact cobordisms
• Multi-toric geometries with larger compact symmetry