Journal of Lie Theory 13 (2003), No. 2, 457--464
Copyright Heldermann Verlag 2003
On the Volume of Unit Vector Fields on a Compact Semisimple Lie Group
Marcos Salvai
FaMAF - CIEM, Ciudad Universitaria, 5000 Cordoba, Argentina
Let G be a compact connected semisimple Lie group endowed with a bi-invariant Riemannian metric. We prove that maximal singular unit vector fields on G are minimal, that is, they are critical points of the volume functional on unit vector fields on G. Besides, we give a lower bound for the number of nonequivalent minimal unit vector fields on G.
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