Abstract
We give the classification of the 3-dimensional contact metric manifolds satisfying ▽ξτ=0, which they have: harmonic curvature, or η-parralel Ricci tensor or cyclic η-parallel Ricci tensor.
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BAIKOUSSIS, C., and KOUFOGIORGOS, T.: On a type of contact manifolds, J. Geom. 46 (1993), 1–9.
BLAIR, D. E.: Contact manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer-Verlag, Berlin, 1976.
BLAIR, D. E., KOUFOGIORGOS, T. and SHARMA, S.: A classification of 3-dimensional contact metric manifolds with Qϕ=ϕQ, Kodai Math. J. 13 (1990), 391–401.
BLAIR, D. E. and SHARMA, R.: Three dimensional locally symmetric contact metric manifolds, Boll. U.M.I. (7) 4-A (1990), 385–390.
BOOTHBY, W. M.: An introduction to differentiable manifolds and Riemannian geometry, Academic Press, Orlando, Florida, 1975.
KOUFOGIORGOS, T.: On a class of contact Riemannian 3-manifolds, Results in Math. 27 (1995), 51–62.
PERRONE, D.: Contact Riemannian manifolds satisfying R(X,ξ)·R=0, Yokohama Math.J., 39 (1992), 141–149.
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Gouli-Andreou, F., Xenos, P.J. On 3-dimensional contact metric manifolds with ▽ξτ=0. J Geom 62, 154–165 (1998). https://doi.org/10.1007/BF01237607
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DOI: https://doi.org/10.1007/BF01237607