Biharmonic maps between warped product manifolds
نویسندگان
چکیده
منابع مشابه
Biharmonic Maps between Doubly Warped Product Manifolds
In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds B and F into the doubly warped product f B ×b F can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections f B ×b F → B and f B ×b F → F , respectively. Some characterizations for non-harmonic biharmonic maps are g...
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A. In this paper, by applying the first variation formula of f -bi-energy given in [OND], we study f -biharmonic maps between doubly warped product manifolds M ×(μ,λ) N. Under imposing existence condition concerning proper f -biharmonic maps, we derive f -biharmonicity’s characteristic equations for the inclusion maps: iy0 : (M, g) → (M ×(μ,λ) N, ḡ), ix0 : (N, h) → (M ×(μ,λ) N, ḡ) and th...
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Let (Mn,g) be a closed Riemannian manifold and N a warped product manifold of two space forms. We investigate geometric properties by the spectra of the Jacobi operator of a harmonic map φ : M → N . In particular, we show if N is a warped product manifold of Euclidean space with a space form and φ,ψ : M → N are two projectively harmonic maps, then the energy of φ and ψ are equal up to constant ...
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and Applied Analysis 3 where TX and NX are the tangential and normal components of FX, respectively, and for V ∈ T⊥M,
متن کاملA Short Survey on Biharmonic Maps between Riemannian Manifolds
and the corresponding Euler-Lagrange equation is H = 0, where H is the mean curvature vector field. If φ : (M, g) → (N, h) is a Riemannian immersion, then it is a critical point of the bienergy in C∞(M,N) if and only if it is a minimal immersion [26]. Thus, in order to study minimal immersions one can look at harmonic Riemannian immersions. A natural generalization of harmonic maps and minimal ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2007
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2006.03.012