Contactly Geodesic Transformations

V. F. Kirichenko ; N. N. Dondukova

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

Résumé

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.

Détail

Keywords: Riemannian manifold, pseudo-Riemannian manifold, geodesic transformation, cosymplectic manifold, Sasakian manifold, Kenmotsu manifold, Riemann–Christoffel tensor, almost-contact structure.