List of ParticipantsOrganizing committee: Vasil Tsanov – Sofia University (Chairman), Harry Aleksiev – High School for Management and Laguages in Zlatograd (Local Organizer), Leon Farhy – Sofia University (Scientific Secretary), Emil Horozov – Sofia University, Ivailo Mladenov – Bulgarian Academy of Sciences, Angel Zhivkov – Sofia University.
Summary: Geometrical concepts induced by a smooth mapping of manifolds with linear connections are introduced, especially the (higher order) covariant differentials of the mapping tangent to and the curvature of a corresponding tensor product connection. As an useful and physically meaningful consequence a basis of differential invariants for natural operators of such smooth mappings is obtained for metric connections. A relation to geometry of Riemannian manifolds is discussed.
A non-holonomic 3-web is defined by two operators and such that is a projector, is involutory, and they are connected via the relation . The so-called parallelizing connection with respect to which the 3-web distributions are parallel is defined. Some simple properties of such connections are found.
Geometric constructions of connections on the higher order principal prolongations of a principal bundle are considered. Moreover, the existing differences among connections on non-holonomic, semiholonomic and holonomic principal prolongations are discussed.