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Matematicheskie Zametki, 2012, Volume 91, Issue 1, Pages 40–53
DOI: https://doi.org/10.4213/mzm8483
(Mi mzm8483)
 

This article is cited in 10 scientific papers (total in 10 papers)

On the Geometry of Normal Locally Conformal Almost Cosymplectic Manifolds

V. F. Kirichenko, S. V. Kharitonova

Moscow State Pedagogical University
References:
Abstract: Normal locally conformal almost cosymplectic structures (or $lc\mathscr{AC_{S}}$-structures) are considered. A full set of structure equations is obtained, and the components of the Riemannian curvature tensor and the Ricci tensor are calculated. Necessary and sufficient conditions for the constancy of the curvature of such manifolds are found. In particular, it is shown that a normal $lc\mathscr{AC_{S}}$-manifold which is a spatial form has nonpositive curvature. The constancy of $\Phi HS$-curvature is studied. Expressions for the components of the Weyl tensor on the space of the associated $G$-structure are obtained. Necessary and sufficient conditions for a normal $lc\mathscr{AC_{S}}$-manifold to coincide with the conformal plane are found. Finally, locally symmetric normal $lc\mathscr{AC_{S}}$-manifolds are considered.
Keywords: normal locally conformal almost cosymplectic structure, Riemannian curvature tensor, Ricci tensor, Weyl tensor, $G$-structure, conformal plane, algebra of smooth structures, module of smooth vector fields, contact form.
Received: 10.04.2009
English version:
Mathematical Notes, 2012, Volume 91, Issue 1, Pages 34–45
DOI: https://doi.org/10.1134/S000143461201004X
Bibliographic databases:
Document Type: Article
UDC: 514.76
Language: Russian
Citation: V. F. Kirichenko, S. V. Kharitonova, “On the Geometry of Normal Locally Conformal Almost Cosymplectic Manifolds”, Mat. Zametki, 91:1 (2012), 40–53; Math. Notes, 91:1 (2012), 34–45
Citation in format AMSBIB
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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