Searcharxiv⌕ Search

arXiv subjects

Abderrahim Zagane

Publications and source records attributed to Abderrahim Zagane.

6 recordsLinked to original sources
arXiv2026

Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric

This work investigates biharmonic and interpolating sesqui-harmonic vector fields on the tangent bundle of a para-Kähler--Norden manifold (M, varphi, g) endowed with the varphi-Sasaki metric. We derive the first variation of the bienergy and interpolating sesqui-energy functionals, restricted to the space of vector fields. Explicit characterizations are established for vector fields satisfying the corresponding variational conditions-namely, biharmonicity and interpolating sesqui-harmonicity. Furthermore, several examples are presented to illustrate the general theory and to elucidate the distinctions between harmonic, biharmonic, and interpolating sesqui-harmonic behaviors. These results extend and complement existing research on higher-order harmonicity in pseudo-Riemannian geometry.

math.DG↗
arXiv2025

Exploring certain geometric and harmonic properties of the Berger-type metric conformal deformation on the Para-Kähler-Norden manifold

This work presents a novel class of metrics on a para-Kähler-Norden manifold $(M^{2m},F,g)$, derived from a conformal deformation of the Berger-type metric associated with the metric $g$. Initially, we examine the Levi-Civita link associated with this metric. Secondly, we delineate all varieties of curvature for a manifold $M$ equipped with a conformal deformation of Berger-type metric for $g$. Finally, we studied a certain class of harmonic maps.

math.DG↗
arXiv2024

Exploring the Cauchy-Riemann structure and integrability conditions of $F$-structures satisfying $αF^{K+1} +βF^{K} + F=0$

This work introduces a new class of $F$-structures satisfying $αF^{K+1} +βF^{K} + F=0$, where $K$ is a positive integer, $K\geq3$, and $α, β$ are real or complex numbers. We investigate the Cauchy-Riemann structure and its link with the $F$-structure. We also address the integrability of this structure, including partial and complete integrability. Finally, we present several examples of the $F$-structure.

math.DG↗
arXiv2023

Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over Kählerian manifold

In this paper, first, we introduce the Berger-type deformed Sasaki metric on the cotangent bundle $T^{\ast}M$ over a Kählerian manifold $(M^{2m}, J, g)$ and investigate the Levi-Civita connection of this metric. Secondly, we present the unit cotangent bundle equipped with Berger-type deformed Sasaki metric, and we investigate the Levi-Civita connection. Finally, we study the geodesics on the cotangent bundle and on unit cotangent bundle with respect to the Berger-type deformed Sasaki metric.

math.DG↗
arXiv2022

Proper biharmonic maps on tangent bundle

This paper, we define the Mus-Gradient metric on tangent bundle $TM$ by a deformation non-conform of Sasaki metric over an n-dimensional Riemannian manifold $(M, g)$. First we investigate the geometry of the Mus-Gradient metric and we characterize a new class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when all of the factors are Euclidean spaces.

math.DG↗