An almost cosymplectic (κ,μ,ν)-space is by definition an almost cosymplectic manifold whose structure tensor fields φ, ξ, η, g satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called -homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields φ, h (), A ( = -∇ξ) fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an almost cosymplectic (κ,μ,ν)-space with κ<0 are locally flat Kählerian manifolds. A local characterization of such manifolds is established up to a -homothetic transformation of the almost cosymplectic structures.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-17,
author = {Piotr Dacko and Zbigniew Olszak},
title = {On almost cosymplectic ($\kappa$,$\mu$,$\nu$)-spaces},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {211-220},
zbl = {1091.53013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-17}
}
Piotr Dacko; Zbigniew Olszak. On almost cosymplectic (κ,μ,ν)-spaces. Banach Center Publications, Tome 68 (2005) pp. 211-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-17/