Abstract.
We show that a locally symmetric contact metric space is either Sasakian and of constant curvature 1 or locally isometric to the unit tangent sphere bundle (with its standard contact metric structure) of a Euclidean space.
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Boeckx, E., Cho, J. Locally Symmetric Contact Metric Manifolds. Mh Math 148, 269–281 (2006). https://doi.org/10.1007/s00605-005-0366-4
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DOI: https://doi.org/10.1007/s00605-005-0366-4