2-harmonic maps and their first and second variational formulas


In [1], J. Eells and L. Lemaire introduced the notion of a k-harmonic map. In this paper we study the case k = 2, derive the first and second variational formulas of the 2-harmonic maps, give nontrivial examples of 2-harmonic maps and give proofs of nonexistence theorems of stable 2-harmonic maps.

DOI Code: 10.1285/i15900932v28n1supplp209

Keywords: harmonic maps; biharmonic maps; second variation formula

Classification: 58E20; 53C43

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