Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 267-274 (1999)

Generalized Hopf Constructions and Eigenmaps between Spheres

Ye-Lin Ou

Department of Mathematics, Guangxi University for Nationalities, 530006 nanning, P. R. China, e-mail:

Abstract: In this paper, we give two kinds of generalizations of Hopf constructions, which can be used to produce many quadratic eigenmaps between spheres (Theorem 2.3) including some well-known examples (e.g. Veronese map) and some new ones. We also obtain some non-existence results (Theorems 3.2, 3.3) for eigenmaps into low dimensional spheres. Finally, we give an existence result (Theorem 3.6) for quadratic eigenmaps $S^{n-2}\times S^1\rightarrow S^{n-1}$.

Keywords: harmonic maps, Hopf constructions, spheres, eigenmaps

Classification (MSC91): 58E20

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