Semisymmetric and semiparallel geodesic spheres and tubes
The authors prove that a connected Riemannian manifold of dimension \(n\) is a real space form if and only if all sufficiently small geodesic spheres or all tubes with sufficiently small radius about all geodesics are semi-parallel for \(n\geq 3\) or Ricci-semi-symmetric for \(n\geq 4\). Several applications are given.
scientific article; zbMATH DE number 941313