Biharmonic maps of cohomogeneity one between spheres (Q645401)

The construction of harmonic joins was invented by \textit{R. T. Smith} [Am. J. Math. 97, 364--385 (1975; Zbl 0321.57020)] and resolved by \textit{W. Ding} [Commun. Math. Phys. 118, No.4, 641--649 (1988; Zbl 0672.58009)] and \textit{V. Pettinati} and \textit{A. Ratto} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 17, No.2, 273--282 (1990; Zbl 0718.58017)]. Using a certain symmetry described by harmonic eigenmaps they reduced the harmonic map equation to an ordinary differential equation. The aim of the present paper is to carry over their methods to the construction of biharmonic maps between spheres. Among the examples constructed here, several are in nontrivial homotopy classes. The constructions are explicit up to solving a fourth order ordinary differential equation.