J. Berndt et al., SYMMETRICAL-LIKE RIEMANNIAN-MANIFOLDS AND GEODESIC SYMMETRIES, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 125, 1995, pp. 265-282
We treat several classes of Riemannian manifolds whose shape operators
of geodesic spheres or Jacobi operators share some properties with th
e ones on symmetric spaces.