This article is cited in 11 papers

Contactly Geodesic Transformations of Almost-Contact Metric Structures

V. F. Kirichenko, N. N. Dondukova

Moscow State Pedagogical University

Abstract: 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.

UDC: 514.7

Received: 16.03.2005

DOI: 10.4213/mzm2802

 English version: Mathematical Notes, 2006, 80:2, 204–213

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