2019/01/15 by Pantilie, Radu
#32L25 #53C26 #53C28 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1901.05072
We introduce the notion of tame ρ-quaternionic manifold that permits the construction of a finite family of ρ-connections, significant for the geometry involved. This provides, for example, the following: (1) a new simple global characterisation of flat (complex-)quaternionic manifolds, and (2) a new simple construction of the metric and the corresponding Levi-Civita connection of a quaternionic-Kähler manifold by starting from its twistor space; moreover, our method provides a natural generalization of this correspondence. Also, a new construction of quaternionic manifolds is obtained, and the properties of twistorial harmonic morphisms with one-dimensional fibres from quaternionic-Kähler manifolds are studied.