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Mat. Zametki, 2006, Volume 80, Issue 2, Pages 209–219 (Mi mz2802)  

This article is cited in 4 scientific papers (total in 4 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

DOI: https://doi.org/10.4213/mzm2802

Full text: PDF file (403 kB)
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English version:
Mathematical Notes, 2006, 80:2, 204–213

Bibliographic databases:

UDC: 514.7
Received: 16.03.2005

Citation: V. F. Kirichenko, N. N. Dondukova, “Contactly Geodesic Transformations of Almost-Contact Metric Structures”, Mat. Zametki, 80:2 (2006), 209–219; Math. Notes, 80:2 (2006), 204–213

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. F. Kirichenko, E. A. Pol'kina, “Geodesic rigidity of certain classes of almost contact metric manifolds”, Russian Math. (Iz. VUZ), 51:9 (2007), 37–44  mathnet  crossref  mathscinet  zmath
    2. L. A. Ignatochkina, “Generalization for transformations of $T^1$-bundle which induced by conformal transformations of their base”, Sb. Math., 202:5 (2011), 665–682  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. V. Nikiforova, “Invarianty obobschennykh $f$-preobrazovanii pochti kontaktnykh metricheskikh struktur”, Chebyshevskii sb., 18:2 (2017), 173–182  mathnet  crossref  elib
    4. A. Abu-Saleem, A. R. Rustanov, S. V. Kharitonova, “Svoistva integriruemosti obobschennykh mnogoobrazii Kenmotsu”, Vladikavk. matem. zhurn., 20:3 (2018), 4–20  mathnet  crossref
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