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Volume-preserving geodesic symmetries on four-dimensional 2-Stein spaces. (English) Zbl 0613.53010

It is an open question whether a Riemannian manifold whose local geodesic symmetries are all volume-preserving is necessarily locally homogeneous. The authors prove this in the case of four-dimensional 2-Stein spaces, the assertion being that the manifold is flat or locally isometric to a rank one symmetric space.
Reviewer: A.Derdzinski

MSC:

53B20 Local Riemannian geometry
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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