**Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 267-274 (1999)
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Generalized Hopf Constructions and Eigenmaps between Spheres

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Ye-Lin Ou

Department of Mathematics, Guangxi University for Nationalities, 530006 nanning, P. R. China, e-mail: ylou@gxu.edu.cn

**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

**Full text of the article:**

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