Transformacións xeodésicas en xeometría cuaterniónica

The notion of a re°ection with respect to a point or a linear subspace of the Euclidean
space has been generalized to that of a geodesic re°ection with respect to a point or a
submanifold in Riemannian manifolds. These local transformations have been broadly
studied not only in the general case but also in the framework of Hermitian, quaternionic
and contact geometry. In many cases, this study leads to nice geometric properties and
to characterizations of special classes of Riemannian manifolds or of special classes of
submanifolds (see, e.g., [CV1], [KPV], [TV] and [V]). In all these studies Jacobi vector
¯elds and normal and Fermi coordinates are basic tools. Among other properties of the
geodesic re°ections isometric, volume-preserving, holomorphic, symplectic and harmonic
ones received special attention.