On the Geometry of Normal Locally Conformal Almost Cosymplectic Manifolds

V. F. Kirichenko   ; S. V. Kharitonova

Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 40-53

Résumé

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.

Détail

Keywords: normal locally conformal almost cosymplectic structure, Riemannian curvature tensor, Ricci tensor, Weyl tensor, algebra of smooth structures, module of smooth vector fields, contact form.
Mots-clés : $G$-structure, conformal plane

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