Journal of Lie Theory
Vol. 13, No. 2, pp. 457--464 (2003)
On the Volume of Unit Vector Fields on a Compact Semisimple Lie Group
Marcos SalvaiMarcos Salvai
Ciudad Universitaria, 5000 Córdoba, Argentina
Abstract: 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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Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.