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p-BIHARMONIC HYPERSURFACES IN EINSTEIN SPACE AND CONFORMALLY FLAT SPACE
Ahmed Mohammed Cherif,Khadidja Mouffoki Korean Mathematical Society 2023 대한수학회보 Vol.60 No.3
In this paper, we present some new properties for p-biharmonic hypersurfaces in a Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces. We present some open problems.
STABLE f-HARMONIC MAPS ON SPHERE
CHERIF, AHMED MOHAMMED,DJAA, MUSTAPHA,ZEGGA, KADDOUR Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.4
In this paper, we prove that any stable f-harmonic map ${\psi}$ from ${\mathbb{S}}^2$ to N is a holomorphic or anti-holomorphic map, where N is a $K{\ddot{a}}hlerian$ manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere ${\mathbb{S}}^2$with Hess $f{\leq}0$. We also prove that any stable f-harmonic map ${\psi}$ from sphere ${\mathbb{S}}^n$ (n > 2) to Riemannian manifold N is constant.
Geometry of Energy and Bienergy Variations between Riemannian Manifolds
CHERIF, AHMED MOHAMED,DJAA, MUSTAPHA Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.3
In this note, we extend the definition of harmonic and biharmonic maps via the variation of energy and bienergy between two Riemannian manifolds. In particular we present some new properties for the generalized stress energy tensor and the divergence of the generalized stress bienergy.
Generalised Ricci Solitons on Sasakian Manifolds
Mekki, Mohammed El Amine,Cherif, Ahmed Mohammed Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.4
In this paper, we show that a Sasakian manifold which also satisfies the generalised gradient Ricci soliton equation, satisfying some conditions, is necessarily Einstein.
Sasakian structures on products of real line and K\"{a}hlerian manifold
Gherici Beldjilali,Ahmed Mohammed Cherif,Kaddour Zaga 강원경기수학회 2019 한국수학논문집 Vol.27 No.4
In this paper, we construct a Sasakian manifold by the product of real line and K\"{a}hlerian manifold with exact K\"{a}hler form. This result demonstrates the close relation between Sasakian and K\"{a}hlerian manifold with exact K\"{a}hler form. We present an example and an open problem.
Stability and Constant Boundary-Value Problems of f-Harmonic Maps with Potential
Kacimi, Bouazza,Cherif, Ahmed Mohammed Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.3
In this paper, we give some results on the stability of f-harmonic maps with potential from or into spheres and any Riemannian manifold. We study the constant boundary-value problems of such maps defined on a specific Cartan-Hadamard manifolds, and obtain a Liouville-type theorem. It can also be applied to the static Landau-Lifshitz equations. We also prove a Liouville theorem for f-harmonic maps with finite f-energy or slowly divergent f-energy.
On the Generalized of p-harmonic and f-harmonic Maps
Embarka Remli,Ahmed Mohammed Cherif 경북대학교 자연과학대학 수학과 2021 Kyungpook mathematical journal Vol.61 No.1
In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.
New Methods of Construction for Biharmonic Maps
Benkartab, Aicha,Cherif, Ahmed Mohammed Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.1
In this paper we study some properties of Riemannian manifolds, we construct a new example of non-harmonic biharmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds.
Biharmonic Submanifolds of Quaternionic Space Forms
Kacimi, Bouazza,Cherif, Ahmed Mohammed Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.4
In this paper, we consider biharmonic submanifolds of a quaternionic space form. We give the necessary and sufficient conditions for a submanifold to be biharmonic in a quaternionic space form, we study different particular cases for which we obtain some non-existence results and curvature estimates.
Geometry of (p, f)-bienergy variations between Riemannian manifolds
Embarka Remli,Ahmed Mohammed Cherif 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.2
In this paper, we extend the definition of the Jacobi operator of smooth maps, and biharmonic maps via the variation of bienergy between two Riemannian manifolds. We construct an example of (p, f)-biharmonic non (p, f)-harmonic map. We also prove some Liouville type theorems for (p, f)-biharmonic maps