On almost cosymplectic (κ,μ,ν)-spaces

Piotr Dacko; Zbigniew Olszak

On almost cosymplectic (κ,μ,ν)-spaces

Piotr Dacko; Zbigniew Olszak

Banach Center Publications (2005)

Volume: 69, Issue: 1, page 211-220
ISSN: 0137-6934

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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 (

= (1 / 2) ℒ_{ξ} φ

), 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.

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Piotr Dacko, and Zbigniew Olszak. "On almost cosymplectic (κ,μ,ν)-spaces." Banach Center Publications 69.1 (2005): 211-220. <http://eudml.org/doc/282258>.

@article{PiotrDacko2005,
abstract = {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 ($= (1/2)ℒ_\{ξ\}φ$), 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.},
author = {Piotr Dacko, Zbigniew Olszak},
journal = {Banach Center Publications},
keywords = {almost cosymplectic manifold; -homothetic transformation; almost cosymplectic ; ; )},
language = {eng},
number = {1},
pages = {211-220},
title = {On almost cosymplectic (κ,μ,ν)-spaces},
url = {http://eudml.org/doc/282258},
volume = {69},
year = {2005},
}

TY - JOUR
AU - Piotr Dacko
AU - Zbigniew Olszak
TI - On almost cosymplectic (κ,μ,ν)-spaces
JO - Banach Center Publications
PY - 2005
VL - 69
IS - 1
SP - 211
EP - 220
AB - 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 ($= (1/2)ℒ_{ξ}φ$), 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.
LA - eng
KW - almost cosymplectic manifold; -homothetic transformation; almost cosymplectic ; ; )
UR - http://eudml.org/doc/282258
ER -

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