Journal of Lie Theory

no. 2
On the Volume of Unit Vector Fields on a Compact Semisimple Lie Group
Journal of Lie Theory, Volume 13 (2003) no. 2, pp. 457-464
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.
DOI: 10.5802/jolt.314
Classification: 22E46, 53C30, 53C35, 53C42
Keywords: semisimple Lie group, minimal unit vector field 
@article{JOLT_2003_13_2_a8,
     author = {M. Salvai},
     title = {On the {Volume} of {Unit} {Vector} {Fields} on a {Compact} {Semisimple} {Lie} {Group}},
     journal = {Journal of Lie Theory},
     pages = {457--464},
     year = {2003},
     volume = {13},
     number = {2},
     doi = {10.5802/jolt.314},
     zbl = {1028.22015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.314/}
}
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M. Salvai. On the Volume of Unit Vector Fields on a Compact Semisimple Lie Group. Journal of Lie Theory, Volume 13 (2003) no. 2, pp. 457-464. doi: 10.5802/jolt.314

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