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SOME RESULTS ON STABLE f-HARMONIC MAPS
Embarka, Remli,Cherif, Ahmed Mohammed Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
In this paper, we prove that any stable f-harmonic map from sphere ${\mathbb{S}}^n$ to Riemannian manifold (N, h) is constant, where f is a smooth positive function on ${\mathbb{S}}^n{\times}N$ satisfying one condition with n > 2. We also prove that any stable f-harmonic map ${\varphi}$ from a compact Riemannian manifold (M, g) to ${\mathbb{S}}^n$ (n > 2) is constant where, in this case, f is a smooth positive function on $M{\times}{\mathbb{S}}^n$ satisfying ${\Delta}^{{\mathbb{S}}^n}(f){\circ}{\varphi}{\leq}0$.
Semi-conformal $L$-harmonic maps and Liouville type theorem
Embarka Remli,Ahmed Mohammed Cherif 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
In this paper, we prove that every semi-conformal harmonic map between Riemannian manifolds is $L$-harmonic map. We also prove a Liouville type theorem for $L$-harmonic maps.
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.
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