Left-invariant minimal unit vector fields on the semi-direct product $\mathbb R^n\rtimes_P\mathbb R$
Bull. Korean Math. Soc. 2010 Vol. 47, No. 5, 951-960
https://doi.org/10.4134/BKMS.2010.47.5.951
Published online September 1, 2010
Seunghun Yi
Youngdong University
Abstract : We provide the set of left-invariant minimal unit vector fields on the semi-direct product $\mathbb R^n\rtimes_P\mathbb R$, where $P$ is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form $\mathbb R^3\rtimes_P\mathbb R$which are unimodular and of type $(R)$.
Keywords : left-invariant minimal unit vector field, Lie group, semi-direct product
MSC numbers : 53C20, 53C25, 53C42
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