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

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Matematicheskie Zametki, 2006, Volume 80, Issue 2, Pages 209–219
DOI: https://doi.org/10.4213/mzm2802 (Mi mzm2802)

This article is cited in 11 scientific papers (total in 11 papers)

Contactly Geodesic Transformations of Almost-Contact Metric Structures

V. F. Kirichenko, N. N. Dondukova

Moscow State Pedagogical University

Full-text PDF (403 kB) Citations (11)

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

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.

Received: 16.03.2005

English version:
Mathematical Notes, 2006, Volume 80, Issue 2, Pages 204–213
DOI: https://doi.org/10.1007/s11006-006-0129-0

Bibliographic databases:

UDC: 514.7

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm2802

https://doi.org/10.4213/mzm2802

https://www.mathnet.ru/eng/mzm/v80/i2/p209

This publication is cited in the following 11 articles:

O. E. Arseneva, M. B. Banaru, M. P. Burlakov, N. I. Guseva, A. R. Rustanov, S. V. Kharitonova, A.M. Shelekhov, “Vadim Fedorovich Kirichenko”, Materialy Mezhdunarodnoi konferentsii «Klassicheskaya i sovremennaya geometriya», posvyaschennoi 100-letiyu so dnya rozhdeniya professora Levona Sergeevicha Atanasyana (15 iyulya 1921 g.—5 iyulya 1998 g.). Moskva, 1–4 noyabrya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 220, VINITI RAN, M., 2023, 3–16
Mohammed Y. Abass, “A Review on Cartan's Structure Equations for Certain Classes of Almost Contact Metric Manifolds”, Basrah Researches Sciences, 49.2:2 (2023), 1
M. Y. Abass, Q. S. Al-Zamil, “On Weyl tensor of $\mathrm{ACR}$ -manifolds of class $C_{12}$ with applications”, Izv. IMI UdGU, 59 (2022), 3–14
Aligadzhi Rustanov, “Nearly Cosymplectic Manifolds of Constant Type”, Axioms, 11:4 (2022), 152
Abood H.M., Abass M.Y., “A Study of New Class of Almost Contact Metric Manifolds of Kenmotsu Type”, Tamkang J. Math., 52:2 (2021), 253–266
Blaga A.M., “Conformal and Paracontactly Geodesic Transformations of Almost Paracontact Metric Structures”, Facta Univ-Ser. Math. Informat., 35:1 (2020), 121–130
A Abu-Saleem, I D Kochetkov, A R Rustanov, “Structural tensors of generalized Kenmotsu manifolds”, IOP Conf. Ser.: Mater. Sci. Eng., 918:1 (2020), 012063
A. Abu-Saleem, A. R. Rustanov, S. V. Kharitonova, “Svoistva integriruemosti obobschennykh mnogoobrazii Kenmotsu”, Vladikavk. matem. zhurn., 20:3 (2018), 4–20
A. V. Nikiforova, “Invarianty obobschennykh $f$ -preobrazovanii pochti kontaktnykh metricheskikh struktur”, Chebyshevskii sb., 18:2 (2017), 173–182
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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