Geodesic
Contactly Geodesic Transformations
Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 209-219.

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We introduce the notion of contactly geodesic transformation of the metric of an almost-contact metric structure as a contact analog of holomorphically geodesic transformations of the metric of an almost-Hermitian structure. A series of invariants of such transformations is obtained. We prove that such transformations preserve the normality property of an almost-contact metric structure. We prove that cosymplectic and Sasakian manifolds, as well as Kenmotsu manifolds, do not admit nontrivial contactly geodesic transformations of the metric, which is a contact analog of the well-known result for Kählerian manifolds due to Westlake and Yano.
Keywords: Riemannian manifold, pseudo-Riemannian manifold, geodesic transformation, cosymplectic manifold, Sasakian manifold, Kenmotsu manifold, Riemann–Christoffel tensor, almost-contact structure. 
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V. F. Kirichenko; N. N. Dondukova. Contactly Geodesic Transformations. Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 209-219. http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a6/

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