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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm5249https://doi.org/10.4213/mzm5249 https://www.mathnet.ru/eng/mzm/v86/i1/p126
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Abstract page: | 524 | Full-text PDF : | 209 | References: | 76 | First page: | 10 |
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