Geodesic Mappings Onto Riemannian Manifolds and Differentiability

  title={Geodesic Mappings Onto Riemannian Manifolds and Differentiability},
  author={Irena Hinterleitner and Josef Mike{\vs}},
In this paper we study fundamental equations of geodesic mappings of manifolds with affine connection onto (pseudo-) Riemannian manifolds. We proved that if a manifold with affine (or projective) connection of differentiability class C (r ≥ 2) admits a geodesic mapping onto a (pseudo-) Riemannian manifold of class C, then this manifold belongs to the differentiability classC. From this result follows if an Einstein spaces admits non-trivial geodesic mappings onto (pseudo-) Riemannian manifolds… 
1 Citations