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Matematicheskie Zametki, 2009, Volume 86, Issue 1, Pages 126–138
DOI: https://doi.org/10.4213/mzm5249
(Mi mzm5249)
 

This article is cited in 7 scientific papers (total in 7 papers)

On the Geometry of Locally Conformally Almost Cosymplectic Manifolds

S. V. Kharitonova

Moscow State Pedagogical University
Full-text PDF (503 kB) Citations (7)
References:
Abstract: We obtain the complete group of structure equations of a locally conformally almost cosymplectic structure (an $lc\mathscr{AC_S}$-structure in what follows) and compute the components of the Riemannian curvature tensor on the space of the associated $G$-structure. Normal $lc\mathscr{AC_S}$-structures are studied in more detail. In particular, we prove that the contact analogs of A. Gray's second and third curvature identities hold on normal $lc\mathscr{AC_S}$-manifolds, while the contact analog of A. Gray's first identity holds if and only if the manifold is cosymplectic.
Keywords: locally conformally almost cosymplectic structure, almost contact manifold, Riemann curvature tensor, $G$-structure, conformal transformation, structure equations, Gray's identities.
Received: 11.07.2008
Revised: 09.12.2008
English version:
Mathematical Notes, 2009, Volume 86, Issue 1, Pages 121–131
DOI: https://doi.org/10.1134/S0001434609070116
Bibliographic databases:
UDC: 514.76
Language: Russian
Citation: S. V. Kharitonova, “On the Geometry of Locally Conformally Almost Cosymplectic Manifolds”, Mat. Zametki, 86:1 (2009), 126–138; Math. Notes, 86:1 (2009), 121–131
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm5249
  • https://www.mathnet.ru/eng/mzm/v86/i1/p126
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    Full-text PDF :209
    References:76
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