Boeckx, E.; Cho, J. T. Locally symmetric contact metric manifolds. (English) Zbl 1103.53047 Monatsh. Math. 148, No. 4, 269-281 (2006). In 1962, M. Okumura proved that a locally symmetric Sasakian manifold is of constant curvature \(+1\) [see Tohoku Math. J. 14, 135–145 (1962; Zbl 0119.37701)]. S. Tanno proved the same result for a locally symmetric \(K\)-contact manifold [see Proc. Japan Acad. 43, 581–583 (1967; Zbl 0155.49802)]. D. Blair considered unit tangent sphere bundles with their standard contact metric structure, he showed that these are locally symmetric if and only if the base space is either the sphere \(S^2(1)\) or some Euclidean space [see Geometry and topology, Singapore, World Scientific 1989, 15–30]). Concerning the classification of all locally symmetric contact metric \((2n+1)\)-manifolds, Blair conjectured that “the only two possibilities are contact metric manifolds which are locally isometric to \(S^{2n+1}(1)\) or \(E^{n+1}\times S^n(4)\)” [see D. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics 203. Boston, MA: Birkhäuser (2002; Zbl 1011.53001)]. In the present paper the authors prove this conjecture. Moreover, they remark that their method, which is a computational one, does not offer any geometric insight into the question why local symmetry and the presence of a contact metric structure are “\(incompatible\)”. They raise the question to find a more conceptual proof of their result. The paper is well written, the topic is well explained and motivated. Reviewer: D. Perrone (Lecce) Cited in 1 ReviewCited in 22 Documents MSC: 53D10 Contact manifolds (general theory) 53C35 Differential geometry of symmetric spaces 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:locally symmetric spaces; contact metric spaces Citations:Zbl 0119.37701; Zbl 1011.53001; Zbl 0155.49802 PDFBibTeX XMLCite \textit{E. Boeckx} and \textit{J. T. Cho}, Monatsh. Math. 148, No. 4, 269--281 (2006; Zbl 1103.53047) Full Text: DOI References: [1] Blair DE (1989) When is the tangent sphere bundle locally symmetric? In: Geometry and Topology, pp 15–30. Singapore: World Scientific [2] Blair DE (2001) Riemannian Geometry of Contact and Symplectic Manifolds. Birkhäuser This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.