arXiv subjects
Publications and source records attributed to Mustafa Özkan.
In this paper, we investigate the classification of $H$-tensional hypersurfaces $M$ in a $4$-dimensional space form $N^4(c)$ of constant sectional curvature $c$. Our results show that minimal hypersurfaces are the only $H$-tensional hypersurfaces in $4$-dimensional space forms, thereby providing an affirmative partial answer to Conjecture 3 proposed in \cite{kacimi}.
Let $ψ: (M,g)\longrightarrow (N,h)$ be a smooth map between Riemannian manifolds. The tension field of $ψ$ can be regarded as a map from $(M,g)$ into the Riemannian vector bundle $ψ^{-1}TN$, equipped with the Sasaki metric $G_{S}$. In this paper, we study certain aspects of two types of maps: those whose tension fields are harmonic maps (called $HM$-tensional maps) and those whose tension fields are harmonic sections (called $HS$-tensional maps).
This article deals with the interpolating sesqui-harmonicity of a vector field $X$ viewed as a map from a Riemannian manifold $(M,g)$ to its tangent bundle $TM$ endowed with the Sasaki metric $g_{S}$. We show characterization theorem for $X$ to be interpolating sesqui-harmonic map. We give also the critical point condition which characterizes interpolating sesqui-harmonic vector fields. When $(M,g)$ is compact and oriented and under some conditions, we prove that $X$ is an interpolating sesqui-harmonic vector field (resp. interpolating sesqui-harmonic map) if and only if $X$ is parallel. Moreover, we extend this result for a left-invariant vector field on a Lie group $G$ having a discrete subgroup $Γ$ such that the quotient $Γ\backslash G$ is compact.
In this paper, we study metallic structures, i.e. polynomial structures with the structure polynomial $Q\left( J\right) =J^{2}-aJ-bI$ on manifolds using the metallic ratio, which is a generalization of the Golden proportion. We investigate for integrability and parallelism conditions of metallic structures. Also, we give some properties of the metallic Riemannian metric and an example of the metallic structure.