Almost complex projective structures and their morphisms

Jaroslav Hrdina

Address: Institute of Mathematics, Faculty of Mechanical Engineering Brno University of Technology, Czech Republic


Abstract: We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical generalizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of the so called Weyl connections and preserving of this class turns out to be the necessary and sufficient condition on diffeomorphisms to become homomorphisms or anti-homomorphisms of almost complex projective geometries.

AMSclassification: primary 53B10.

Keywords: linear connection, geodetics, F-planar, A-planar, parabolic geometry, Cartan geometry, almost complex structure, projective structure.