Two natural generalizations of locally symmetric spaces (Q1184554)

The authors study two classes of Riemannian manifolds which extend the class of locally symmetric spaces: manifolds all of whose Jacobi operators along geodesics have constant eigenvalues, or parallel eigenspaces, respectively. Various equivalent characterizations are derived and the classification is done for the two- and the three- dimensional case. This classification is particularly interesting for the second class because it gives close relations to classical concepts such as Liouville surfaces and the Schrödinger equation.