arXiv subjects

Karina Olszak

Publications and source records attributed to Karina Olszak.

4 recordsLinked to original sources

arXiv2019

The equi-affine curvatures of curves in 3-dimensional pseudo-Riemannian manifolds

In this paper, the Cartan frames and the equi-affine curvatures are described with the help of the Frenet frames and the Frenet curvatures of a non-null and non-degenerate curve in a 3-dimensional pseudo-Riemannian manifold. The constancy of the Frenet curvatures of such a curve always implies the constancy of the equi-affine curvatures. We show that the converse statement does not hold in general. Finally, we study the equi-affine curvatures of null curves in 3-dimensional Lorentzian manifolds, and prove that they are related to their pseudo-torsion.

math.DG↗

arXiv2018

The equi-affine and Frenet curvatures of curves in pseudo-Riemannian 2-manifolds

For an arbitrary nondegenerate curve in a pseudo-Riemann\-ian (including Riemannian) 2-manifold, we express the equi-affine curvature with the help of the Frenet (geodesic) curvature of this curve.

math.DG↗

arXiv2011

On pseudo-Riemannian manifolds with recurrent concircular curvature tensor

It is proved that every concircularly recurrent manifold must be necessarily a recurrent manifold.

math.DG↗

arXiv2011

On 4-dimensional, conformally flat, almost $ε$-Kählerian manifolds

The local structure of 4-dimensional, conformally flat, almost $ε$-Kählerian (i.e., almost pseudo-Kählerian and almost para-Kählerian) manifolds is characterized with the help of left-regular and right-regular paraquaternionic functions. Examples of such structures are discussed.

math.DG↗