arXiv subjects

Sadık Keleş

Publications and source records attributed to Sadık Keleş.

6 recordsLinked to original sources

arXiv2012

Warped product submanifolds of Lorentzian paracosymplectic manifolds

In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {$M=M_{T}\times_{f}M_{\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to $M$ is an usual Riemannian product manifold where totally geodesic and totally umbilical submanifolds of warped product are invariant and anti-invariant, respectively. We prove that the distributions involved in the definition of a warped product semi-invariant submanifold are always integrable. A necessary and sufficient condition for a semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be warped product semi-invariant submanifold is obtained. We also investigate the existence and nonexistence of warped product semi-slant and warped product anti-slant submanifolds in a Lorentzian paracosymplectic manifold.

math.DG↗

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↗

arXiv2009

On $(\varepsilon)$-para Sasakian 3-manifolds

In this paper we study the 3-dimensional $(\varepsilon) $-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon ) $-para Sasakian 3 -manifold to be an indefinite space form. We show that a Ricci-semi-symmetric $(\varepsilon) $-para Sasakian 3 -manifold is an indefinite space form. We investigate the necessary and sufficient condition for an $(\varepsilon) $-para Sasakian 3 -manifold to be locally $φ$-symmetric. It is proved that in an $ (\varepsilon) $-para Sasakian 3-manifold with $η$ -parallel Ricci tensor the scalar curvature is constant. It is also shown that every $(\varepsilon) $-para Sasakian 3-manifolds is pseudosymmetric in the sense of R. Deszcz.

math.DG↗

arXiv2009

Biharmonic curves on \textit{LP}-Sasakian manifolds

In this paper we give necessary and sufficient conditions for spacelike and timelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional \textit{LP}-Sasakian manifold to be proper biharmonic. Also, we investigate proper biharmonic curves in the Lorentzian sphere $S^{4}_{1}$.

math.DG↗