The Levi-Civita geodesic equivalence problem and multiplication of cofactor pair systems

Abstract: When studying equivalence of dynamical systems, in the sense of Levi-Civita, the concept of cofactor pair systems plays an important role. Co-factor pair systems can be constructed through a multiplicative structure of the so called quasi-Cauchy-Riemann equations (cof J)-1▽V = (cof )-1▽, where J and are special conformal Killing tensors. In this thesis we study this multiplication and its role in the theory of equivalentdynamical systems. We have isolated the properties that are responsible for the multiplication, allowing us to give an elegant characterization of systems that admit multiplication. We describe how the multiplication of cofactor pair systems can be considered as a special case of a more general kind of multiplication. We also investigate algebraic properties of the multiplication and provide several methods for constructing new systems with multiplicative structure.