2 research outputs found
Geodesic mappings of (pseudo-) Riemannian manifolds preserve the class of differentiability
In this paper we prove that geodesic mappings of (pseudo-) Riemannian
manifolds preserve the class of differentiability \hbox{}. Also,
if the Einstein space admits a non trivial geodesic mapping onto a
\hbox{(pseudo-)} Riemannian manifold , then is an
Einstein space.
If a four-dimensional Einstein space with non constant curvature globally
admits a geodesic mapping onto a (pseudo-) Riemannian manifold , then the mapping is affine and, moreover, if the scalar curvature is non
vanishing, then the mapping is homothetic, i.e. .Comment: 8 page
Invariants of Third Type Almost Geodesic Mappings of Generalized Riemannian Space
We studied rules of transformations of Christoffel symbols under third type
almost geodesic mappings in this paper. From this research, we obtained some
new invariants of these mappings. These invariants are analogies of Thomas
projective parameter and Weyl projective tensor.Comment: 10 pages, 0 figures, manuscrip