Harmonic Hopf Constructions between Spheres Ii
نویسندگان
چکیده
This paper can be seen as the final remark of the previous paper written by the first author [D]. We consider the existence of harmonic maps between two spheres, via Hopf constructions. Given a non trivial bi-eigenmap f : S × S −→ S with bi-eigenvalue (λ, μ) (λ, μ > 0) and a continuous function α : [ 0, 2 ]−→ [ 0, π ] with α(0) = 0 , α(2 ) = π , one defines a map u: S p+q+1 −→ S , called the α-Hopf construction on f, by u(sin t · x, cos t · y) = (sinα(t)f(x, y), cosα(t)), where x ∈ S, y ∈ S and t ∈ [0, 2 ]. It is known [ER] that u is a harmonic map if and only if α is a solution of the o.d.e.
منابع مشابه
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تاریخ انتشار 1994