Conformal Derivative and Conformal Transports over (l N , G) Spaces

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as " conformal " transports and investigated over (Ln, g)-spaces. They are more general than the Fermi-Walker transports. In an analogous way as in the case of Fermi-Walker transports a conformal covariant differential operator and its conformal derivative are defined and considered over (Ln, g)-spaces. Different special types of conformal transports are determined inducing also Fermi-Walker transports for orthogonal vector fields as special cases. Conditions under which the length of a non-null contravariant vector field could swing as a homogeneous harmonic os-cillator are established. The results obtained regardless of any concrete field (gravitational) theory could have direct applications in such types of theories.