This article is cited 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.

UDC: 514.76

Received: 11.07.2008
Revised: 09.12.2008

DOI: 10.4213/mzm5249

 English version: Mathematical Notes, 2009, 86:1, 121–131

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