Geodesic Mapping Invariants: From Weyl’s to Current Techniques

Abstract

In this paper, we study invariants of geometric mappings in affine connection spaces,
with a particular focus on geodesic mappings as a special case. We revisit the classical
methodology for finding invariants and extend it to generalized affine connection spaces
(with torsion). By analyzing the difference between affine connection coefficients of two
spaces, we explicitly construct the Thomas projective parameter and the Weyl projective
tensor, which provide fundamental invariants under geodesic mappings. We also
investigate the role of torsion in these constructions.