SOME VECTORS FIELDS ON THE TANGENT BUNDLE WITH A SEMI-SYMMETRIC METRIC CONNECTION

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic vector fields, concurrent vector fields, conformal vectorfields and projective vector fields on $TM$ with respect to thesemi-symmetric metric connection $\overline{\nabla }$ and obtain someproperties related to them

Notes concerning K\"ahler and anti-K\"ahler structures on quasi-statistical manifolds

Let $(\acute{N},g,\nabla )$\ be a $2n$-dimensional quasi-statistical manifold that admits a pseudo-Riemannian metric $g$ (or $h)$ and a linear connection $\nabla$ with torsion. This paper aims to study an almost Hermitian structure $(g,L)$ and an almost anti-Hermitian structure $(h,L)$ on a quasi-statistical manifold that admit an almost complex structure $L$. Firstly, under certain conditions, we present the integrability of the almost complex structure $L$. We show that when $d^\nabla L =0$ and the condition of torsion-compatibility are satisfied, $(\acute{N},g,\nabla ,$ $L)$ turns into a K\"{a}hler manifold. Secondly, we give necessary and sufficient conditions under which $(\acute{N},h,\nabla ,L)$ is an anti-K\"{a}% hler manifold, where $h$ is an anti-Hermitian metric. Moreover, we search the necessary conditions for $(\acute{N},h,\nabla ,L)$ to be a quasi-K\"{a}hler-Norden manifold

ON THE COTANGENT BUNDLE AND UNIT COTANGENT BUNDLE WITH A GENERALIZED CHEEGER-GROMOLL METRIC

In this paper, we consider a generalized Cheeger-Gromoll metric on a cotangent bundle over a Riemannian manifold, which is obtained by rescaling the vertical part of the Cheeger-Gromoll metric by a positive dierentiable function. Firstly, we investigate the curvature properties on the cotangent bundle with the generalized Cheeger-Gromoll metric. Secondly, we introduce the unit cotangent bundle equipped with this metric, where we present the formulas of the Levi-Civita connection and also all formulas of the Riemannian curvature tensors of this metric. Finally, we study the geodesics on the unit cotangent bundle with respect to this metric

Sixth, seventh and eighth year students' knowledge levels about greenhouse effect, ozone layer and acid rain

The aim of this study is to investigate second stage primary school (6th, 7th and 8th year) students’ knowledge levels about three important environmental topics, namely, the greenhouse effect, the ozone layer and acid rain. The study was carried out with 204 6th, 7th and 8th year students (11-14 year olds) in Turkey. A 25- item scale developed by Khalid (1999) was used as a data collection instrument. The instrument was adapted to the Turkish language and culture, was validated and its reliability co-efficiency was determined. The results of the study showed that 6th, 7th and 8th year students have a very low level of knowledge about the greenhouse effect, the ozone layer and acid rain. The results of this study can be used by experts of environmental education to focus on starting the teaching of environmental topics – like greenhouse effect, ozone layer and acid rain – thoroughly from the primary school to develop more environmentally sensitive citizens.peer-reviewe