# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## On almost cosymplectic $(\kappa,\mu,\nu)$-spaces

### Tom 69 / 2005

Banach Center Publications 69 (2005), 211-220 MSC: Primary 53C25; Secondary 53D15. DOI: 10.4064/bc69-0-17

#### Streszczenie

An almost cosymplectic $(\kappa,\mu,\nu)$-space is by definition an almost cosymplectic manifold whose structure tensor fields $\varphi$, $\xi$, $\eta$, $g$ satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called $\mathcal D$-homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields $\varphi$, $h$ $(=(1/2)\mathcal L_{\xi}\varphi)$, $A$ $(=-\nabla\xi)$ fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an almost cosymplectic $(\kappa,\mu,\nu)$-space with $\kappa<0$ are locally flat Kählerian manifolds. A local characterization of such manifolds is established up to a $\mathcal D$-homothetic transformation of the almost cosymplectic structures.

#### Autorzy

• Piotr DackoInstitute of Mathematics and Informatics
Wroc/law University of Technology
Wybrzeże Wyspiańskiego 27
50-370 Wroc/law, Poland
e-mail
• Zbigniew OlszakInstitute of Mathematics and Informatics
Wroc/law University of Technology
Wybrzeże Wyspiańskiego 27
50-370 Wroc/law, Poland
e-mail

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