Tsukuba Journal of Mathematics

On almost para-cosymplectic manifolds

Piotr Dacko

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Abstract

An almost para-cosymplectic manifold is by definition an odd-dimensional differentiable manifold endowed with an almost paracontact stmcture with hyperbolic metric for which the structure forms are closed. The local structure of an almost para-cosymplectic manifold is described. We also treat some special subclasses of this class of manifolds: para-cosymplectic, weakly para-cosymplectic and almost para-cosymplectic with para-Kählerian leaves. Necessary and sufficient conditions for an almost para-cosymplectic manifold to be para-cosymplectic are found. Necessary and sufficient conditions for an almost para-cosymplectic manifold with para-Kählerian leaves to be weakly para-cosymplectic are also established. We construct examples of weakly para-cosymplectic manifolds, which are not paracosymplectic. It is proved that in dimensions $\geq 5$ an almost paracosymplectic manifold cannot be of non-zero constant sectional curvature. Main curvature identities which are fulfilled by any almost para-cosymplectic manifold are found.

Article information

Source
Tsukuba J. Math., Volume 28, Number 1 (2004), 193-213.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496164721

Digital Object Identifier
doi:10.21099/tkbjm/1496164721

Mathematical Reviews number (MathSciNet)
MR2082229

Zentralblatt MATH identifier
1076.53033

Citation

Dacko, Piotr. On almost para-cosymplectic manifolds. Tsukuba J. Math. 28 (2004), no. 1, 193--213. doi:10.21099/tkbjm/1496164721. https://projecteuclid.org/euclid.tkbjm/1496164721


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