Illinois Journal of Mathematics

Minimality and harmonicity for Hopf vector fields

K. Tsukada and L. Vanhecke

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We determine when the Hopf vector fields on orientable real hypersurfaces $(M,g)$ in complex space forms are minimal or harmonic. Furthermore, we determine when these vector fields give rise to harmonic maps from $(M,g)$ to the unit tangent sphere bundle $(T_1M,g_S)$. In particular, we consider the special case of Hopf hypersurfaces and of ruled hypersurfaces. The Hopf vector fields on Hopf hypersurfaces with constant principal curvatures provide examples. The minimal ruled real hypersurfaces form another class of particular examples.

Article information

Illinois J. Math., Volume 45, Number 2 (2001), 441-451.

First available in Project Euclid: 13 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]
Secondary: 58E20: Harmonic maps [See also 53C43], etc.


Tsukada, K.; Vanhecke, L. Minimality and harmonicity for Hopf vector fields. Illinois J. Math. 45 (2001), no. 2, 441--451. doi:10.1215/ijm/1258138349.

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