f -BIHARMONIC MAPS BETWEEN DOUBLY WARPED PRODUCT MANIFOLDS
نویسنده
چکیده
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 the product maps: Ψ = IdM × φN : M ×(μ,λ) N → M × N, Ψ̃ = ̃ φM × IdN : M ×(μ,λ) N → M × N with φM φN being a harmonic map.
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