GEODESIC TRANSFORMATIONS AND SPACE FORMS

We introduce the notion of a geodesic transformation with respect to a submanifold P of a Riemannianmanifold as a generalization of a geodesic reflection with respect to P. We study conformal and partiallyconformal geodesic transformation with respect to points and geodesic spheres, and use these kinds of transformationto characterize real, complex and quaternionic space forms by means of non-Euclidean similaritiesand inversions