GEODESIC MAPPINGS OF (PSEUDO-) RIEMANNIAN MANIFOLDS PRESERVE CLASS OF DIFFERENTIABILITY.

In this paper, we prove that geodesic mappings of (pseudo-) Riemannian manifolds preserve the class of differentiability (Cr , r ≥ 1). Also, if the Einstein space Vn admits a nontrivial geodesic mapping onto a (pseudo-) Riemannian manifold ̄Vn ∈ C1, then VNn is an Einstein space. If a four-dimensional Einstein space with non-constant curvature globally admits a geodesic mapping onto a (pseudo-) Riemannian manifold ̄V4 ∈ C1, then the mapping is affine and, moreover, if the scalar curvature is non-vanishing, then the mapping is homothetic, i. e. ̄g D const · g. [ABSTRACT FROM AUTHOR]