Two natural generalizations of locally symmetric spaces. (English) Zbl 0747.53013
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.
Reviewer: O.Kowalski (Praha)
MSC:
| 53B20 | Local Riemannian geometry |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C35 | Differential geometry of symmetric spaces |
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