On tame $\rho$-quaternionic manifolds

20 Jun 2019  ·  Pantilie Radu ·

We introduce the notion of tame $\rho$-quaternionic manifold that permits the construction of a finite family of $\rho$-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-K\"ahler 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-K\"ahler manifolds are studied. read more

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Differential Geometry Algebraic Geometry