arXiv subjects

Mehmet Göçmen

Publications and source records attributed to Mehmet Göçmen.

3 recordsLinked to original sources

arXiv2011

Notes on Degenerate Curves in Pseudo-Euclidean Spaces of Index Two

In this paper we deal with curves with degeneration degree two in pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the $6-$dimensional pseudo-Euclidean space of index two. Also we characterize pseudo-spherical null curves in the $n-$dimensional pseudo-Euclidean space of index two in terms of the curvature functions.

math.DG↗

arXiv2011

2-Degenerate Bertrand curves in Minkowski spacetime

In this paper we define a new type of 2-degenerate Cartan curves in Minkowski spacetime $R_{1}^{4}$. We prove that this type of curves contain only the polynomial functions as its components whose third derivative vanish completely. No curve with acceleration zero in $R_{1}^{4}$ is a 2-degenerate Cartan curve, therefore we show that the type of curves that we search for must contain polynomials of degree two among its components.

math.DG↗

arXiv2011

$(1,2)$-Null Bertrand Curves in Minkowski Spacetime

In this paper we study null Bertrand curves in $R_{1}^{4}$ under the assumption the curve has a Cartan frame. We show that if the derivative vectors of the null Cartan curve in $R_{1}^{4}$ is linearly independent, then this curve is not a Bertrand curve. Since then the already known notion of null Bertrand curves in $R_{1}^{4}$ occurs only if the derivative vectors of the curve is linearly dependent. We will introduce an idea of Bertrand curves and abiding by this idea we bring to light under which conditions a null Cartan curve in $R_{1}^{4}$ is a Bertrand curve.

math.DG↗