Unit vector fields that are critical points of the volume and of the energy: characterization and examples. (English) Zbl 1075.53055

Kowalski, Oldřich (ed.) et al., Complex, contact and symmetric manifolds. In honor of L. Vanhecke. Selected lectures from the international conference “Curvature in Geometry” held in Lecce, Italy, June 11–14, 2003. Boston, MA: Birkhäuser (ISBN 0-8176-3850-4/hbk). Progress in Mathematics 234, 165-186 (2005).
The paper provides known examples and general results on harmonicity and minimality of vector fields in different geometric situations. It contains definitions and characterization of critical vector fields, results concerning the volume and the energy of vector fields, and numerous examples regarding: vector fields on Lie groups and homogeneous spaces, examples from contact geometry, results on the Hopf vector field of a hypersurface of a complex manifold, and on unit vector fields on tangent and unit tangent bundles.
For the entire collection see [Zbl 1062.53001].


53C43 Differential geometric aspects of harmonic maps
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)