## Illinois Journal of Mathematics

### Minimality and harmonicity for Hopf vector fields

#### Abstract

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

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

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138349

Digital Object Identifier
doi:10.1215/ijm/1258138349

Mathematical Reviews number (MathSciNet)
MR1878613

Zentralblatt MATH identifier
0997.53040

#### Citation

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. https://projecteuclid.org/euclid.ijm/1258138349