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Şaban Güvenç

Publications and source records attributed to Şaban Güvenç.

9 recordsLinked to original sources
arXiv2025

Biharmonic Curves in Warped Product Manifolds $I\times_{f}M^{n}\left( c\right) $

We explore the geometric properties of biharmonic curves in warped product manifolds of the form $I\times _{f}M^{n}(c)$, where $I$ is an open interval and $M^{n}(c)$ is a space of constant curvature. By establishing a main theorem, we analyze four distinct cases to reveal deeper curvature-related characteristics of these curves, including situations where they are slant. Finally, we construct two examples in $I\times _{f}S^{2}(1)$.

math.DG↗
arXiv2024

Unveiling $f-$Biharmonic $θ_{α}-$Slant Curves in $\mathcal{S}-$ Space Forms

In this paper, we firstly provide a concise overview of $\mathcal{S}-$manifolds, $f$-biharmonicity and $θ_{α}$-slant curves. We then derive a key equation and analyze it in detail to establish the necessary and sufficient conditions for $θ_{α}$-slant curves to be $f$-biharmonic. Finally, we present an example to support our findings.

math.DG↗
arXiv2021

New Fixed Figure Results with the Notion of $k$-Ellipse

In this paper, as a geometric approach to the fixed-point theory, we prove new fixed-figure results using the notion of $k$-ellipse on a metric space. For this purpose, we are inspired by the Caristi type contraction, Kannan type contraction, Chatterjea type contraction and Ćirić type contraction. After that, we give some existence and uniqueness theorems of a fixed $k$-ellipse. We also support our obtained results with illustrative examples. Finally, we present a new application to the $S$-Shaped Rectified Linear Activation Unit ($SReLU$) to show the importance of our theoretical results.

math.MG↗
arXiv2021

Magnetic Curves in $C$-manifolds

In this paper, we study normal magnetic curves in $C$-manifolds. We prove that magnetic trajectories with respect to the contact magnetic fields are indeed $θ_{α}$-slant curves with certain curvature functions. Then, we give the parametrizations of normal magnetic curves in $\mathbb{R}^{2n+s}$ with its structures as a $C$-manifold.

math.DG↗
arXiv2021

Legendre Trajectories of Trans-$S$-Manifolds

In this paper, we consider Legendre trajectories of trans-$S$-manifolds. We obtain curvature characterizations of these curves and give a classification theorem. We also investigate Legendre curves whose Frenet frame fields are linearly dependent with certain combination of characteristic vector fields of the trans-$S$-manifold.

math.DG↗
arXiv2020

On Pseudo-Hermitian Magnetic Curves in Sasakian Manifolds

We define pseudo-Hermitian magnetic curves in Sasakian manifolds endowed with the Tanaka-Webster connection. After we give a complete classification theorem, we construct parametrizations of pseudo-Hermitian magnetic curves in $\mathbb{R}^{2n+1}(-3)$.

math.DG↗
arXiv2019

On Slant Magnetic Curves in $S$-manifolds

We consider slant normal magnetic curves in $(2n+1)$-dimensional $S$-manifolds. We prove that $γ$ is a slant normal magnetic curve in an $% S $-manifold $(M^{2m+s},φ,ξ_{α},η^{α},g)$ if and only if it belongs to a list of slant $φ$-curves satisfying some special curvature equations. This list consists of some specific geodesics, slant circles, Legendre and slant helices of order $3$. We construct slant normal magnetic curves in $\mathbb{R}^{2n+s}(-3s)$ and give the parametric equations of these curves.

math.GM↗
arXiv2019

$C$-parallel and $C$-proper Slant Curves of $S$-manifolds

In the present paper, we define and study $C$-parallel and $C$-proper slant curves of $S$-manifolds. We prove that a curve $γ$ in an $S$-manifold of order $r\geq 3,$ under certain conditions, is $C$-parallel or $C$-parallel in the normal bundle if and only if it is a non-Legendre slant helix or Legendre helix, respectively. Moreover, under certain conditions, we show that $γ$ is $C$-proper or $C$-proper in the normal bundle if and only if it is a non-Legendre slant curve or Legendre curve, respectively. We also give two examples of such curves in $\mathbb{R}^{2m+s}(-3s).$

math.GM↗