Recent advances in the theory of holonomy
The biregular functions in the sense of Fueter are investigated. In particular, the class of LR-biregular mappings (left regular with a right regular inverse) is introduced. Moreover, the existence of non-affine biregular mappings is established via examples. Some applications to the quaternionic manifolds are given.
We consider symmetries on filtered manifolds and we study the -graded parabolic geometries in more details. We discuss the existence of symmetries on the homogeneous models and we conclude some simple observations on the general curved geometries.