Geodesic
φ-symmetriccontact metric spaces
Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 409-416

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We give thefirst examples of contact metric spaces which are weakly locally$\varphi$-symmetric (that is, $\nabla R=0$ on horizontal vectors), butnot strongly (that is, not all reflections with respect to thecharacteristic lines are local isometries). These examples arethree-dimensional non-unimodular Lie groups with a left-invariantcontact metric structure. We exhibit additional symmetries on thesespaces.1991 Mathematics Subject Classification: 53B20,53C15, 53C25. 
Boeckx, E.; Bueken, P.; Vanhecke, L. φ-symmetriccontact metric spaces. Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 409-416. doi: 10.1017/S0017089599000579
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     title = {\ensuremath{\varphi}-symmetriccontact metric spaces},
     journal = {Glasgow mathematical journal},
     pages = {409--416},
     year = {1999},
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     doi = {10.1017/S0017089599000579},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089599000579/}
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