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Cihan Özgür

Publications and source records attributed to Cihan Özgür.

15 recordsLinked to original sources
arXiv2026

Generalized Wintgen inequalities for submanifolds of conformally flat manifolds

We obtain generalized Wintgen inequalities for submanifolds of conformally flat manifolds. As applications, we derive corresponding inequalities for submanifolds of Riemannian manifolds of quasi-constant curvature, generalized Robertson--Walker type warped products, conformally changed real space forms, and products of real space forms with opposite curvatures. Equality cases are also discussed. Moreover, several obstructions to the existence of minimal submanifolds are obtained from these inequalities.

math.DG↗
arXiv2025

Hypersurfaces in Riemannian manifolds with torse-forming axes

In this paper, we study orientable hypersurfaces $N$ in Riemannian manifolds $(M,\langle , \rangle)$ for which the inner product $\langle U, \mathcal{V} \rangle$ is constant, where $U$ is the unit normal vector field to $N$ and $\mathcal{V}$ is a globally defined torse-forming vector field on $M$, called the axis of $N$. When $\mathcal{V}$ is a unit torse-forming vector field, $N$ becomes a constant angle hypersurface with axis $\mathcal{V}$, and we classify such hypersufaces. After that, the case when $\mathcal{V}$ is a torqued vector field is considered and a corresponding classification is given.

math.DG↗
arXiv2025

Torqued and Anti-Torqued Vector Fields on Hyperbolic Spaces

In this paper, we study the existence of torqued and anti-torqued vector fields on the hyperbolic ambient space $\mathbb{H}^n$. Although there are examples of proper torqued vector fields on open subsets of $\mathbb{H}^n$, we prove that there is not a proper torqued vector field globally defined on $\mathbb{H}^n$. Similarly, we have another non-existence result for anti-torqued vector fields as long as their conformal scalar is a non-constant function satisfying certain conditions. When the conformal scalar is constant, some examples of anti-torqued vector fields are provided.

math.DG↗
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↗
arXiv2025

Some properties of hyperbolic Yamabe solitons

We define the hyperbolic Yamabe flow and obtain some properties of its stationary solutions, namely, of hyperbolic Yamabe solitons. We consider immersed submanifolds as hyperbolic Yamabe solitons and prove that, under certain assumptions, a hyperbolic Yamabe soliton hypersurface is a pseudosymmetric or a metallic shaped hypersurface. We characterize the hyperbolic Yamabe soliton factor manifolds of a multiply twisted, multiply warped, doubly warped, and warped product manifold and provide a classification for a complete gradient hyperbolic Yamabe soliton factor manifold. We also determine the conditions for the factor manifolds to be hyperbolic Yamabe solitons if the manifold is a hyperbolic Yamabe soliton and illustrate this result for a physical model of the universe, namely, for the Robertson--Walker spacetime.

math.DG↗
arXiv2025

Anti-torqued slant helices and Torqued Curves in Riemannian manifolds

In this paper, we introduce the notion of an anti-torqued slant helix in a Riemannian manifold, defined as a curve whose principal vector field makes a constant angle with an anti-torqued vector field globally defined on the ambient manifold. We characterize and classify such curves through systems of differential equations involving their invariants. Several illustrative examples are also provided. Finally, we study torqued curves, defined as curves for which the inner product function of the principal vector field and a torqued vector field along the curve is a given constant.

math.DG↗
arXiv2024

Rectifying submanifolds of Riemannian manifolds with anti-torqued axis

In this paper we study rectifying submanifolds of a Riemannian manifold endowed with an anti-torqued vector field. For this, we first determine a necessary and sufficient condition for the ambient space to admit such a vector field. Then we characterize submanifolds for which an anti-torqued vector field is always assumed to be tangent or normal. A similar characterization is also done in the case of the torqued vector fields. Finally, we obtain that the rectifying submanifolds with anti-torqued axis are the warped products whose warping function is a first integration of the conformal scalar of the axis.

math.DG↗
arXiv2021

H-almost Ricci-Yamabe solitons in paracontact geometry

In this article, we classify h-almost Ricci-Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci-Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci-Yamabe solitons. Next, we classify para-Sasakian manifolds admitting h-almost Ricci-Yamabe solitons and h-almost gradient Ricci-Yamabe solitons. Besides these, we investigate h-almost Ricci-Yamabe solitons and h-almost gradient Ricci-Yamabe solitons in para-cosymplectic manifolds. Finally, we construct two examples to illustrate our results.

math.DG↗
arXiv2020

Almost $η$-Ricci and almost $η$-Yamabe solitons with torse-forming potential vector field

We provide properties of almost $η$-Ricci and almost $η$-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold $\left(\widetilde{M},\widetilde{g} \right)$ whose potential vector field is the tangential component of a torse-forming vector field on $\widetilde{M}$, treating also the case of a minimal or pseudo quasi-umbilical hypersurface. Moreover, we give necessary and sufficient conditions for an orientable hypersurface of the unit sphere to be an almost $η$-Ricci or an almost $η$-Yamabe soliton in terms of the second fundamental tensor field.

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 C-Parallel Legendre Curves in Non-Sasakian Contact Metric Manifolds

In $(2n+1)$-dimensional non-Sasakian contact metric manifolds, we consider Legendre curves whose mean curvature vector fields are $\mathcal{C}$-parallel or $\mathcal{C}$-proper in the tangent or normal bundles. We obtain the curvature characterizations of these curves. Moreover, we give some examples of these kinds of curves which satisfy the conditions of our results.

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↗
arXiv2019

On Interpolating Sesqui-Harmonic Legendre Curves in Sasakian Space Forms

We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain an example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.

math.DG↗