Geometry of almost Cliffordian manifolds

Jaroslav Hrdina, Brno University of Technology, Czech Republic

We deals with Clifford algebras and geometric structures over them. Motivated by the fact that the choice of the projective structure corresponds to the choice of the class of connections sharing geodesics and the choice of "complex" projective structure corresponds to the choice of connections sharing the $J$-planar curves, we define the projective $A$-structures as $A$-structures together with the choice of connection class sharing $A$-planar curves. If $A$ is a Clifford algebra, we obtain a class of so called Cliffordian projective structures.