Geodesic
On $K$-contact metric structures
Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 23 (1997), pp. 43-55

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We obtain a complete system of structure equations of $K$-contact manifolds and study connections between various characteristics of isotropy of $K$-contact manifolds: the constancy of $\Phi$-sectional curvature, the axiom of $\Phi$-holomorphic planes, etc. We prove that a $K$-contact manifold is locally symmetric if and only if this manifold is conformally flat, and obtain a complete classification of such manifolds. 
@article{KUTGS_1997_23_a4,
     author = {N. V. Ermak},
     title = {On $K$-contact metric structures},
     journal = {Trudy Geometricheskogo Seminara},
     pages = {43--55},
     publisher = {mathdoc},
     volume = {23},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/KUTGS_1997_23_a4/}
}
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N. V. Ermak. On $K$-contact metric structures. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 23 (1997), pp. 43-55. http://geodesic.mathdoc.fr/item/KUTGS_1997_23_a4/