Resumen de Nonlinear connections for conformal gauge theories on path-spaces and duality

Mircea Crasmareanu

• Weyl structures and compatible nonlinear connections are introduced in the ge- ometry of semisprays as a natural generalization of similar notions from Riemannian geometry. The existence and formula for the set of all compatible nonlinear connec- tions are derived by using the Obata tensors naturally associated to a xed metric in the given conformal class; this formula is also expressed in terms of dual non- linear connections which generalize the Norden's notion of dual linear connections.

  A geometric meaning for pairs (Weyl structure, compatible nonlinear connection) is provided in terms of gauge conformal invariance.