Abstract
The aim of this work is to completely describe two families of Lie algebras whose Lie groups have negative sectional curvature. The first family consists of Lie algebras satisfying the following property: given any two vectors in the Lie algebra, the linear subspace spanned by them is a Lie subalgebra. On the other hand, the second family consists of reduced Lie algebras of Iwasawa type.
Publisher
Universidad Industrial de Santander
Reference15 articles.
1. Azencott R. and Wilson E.N., "Homogeneous manifols with negative curvature. I", Trans. Amer. Math. Soc., 215 (1976), 323-362. doi: 10.1090/S0002-9947-1976-0394507-4
2. Barnet F., "On Lie groups that admit Left-invariant Lorentz metrics of constant sectional curvature", Illinois J. of Math., 33 (1989), No. 4, 631-642. doi: 10.1215/ijm/1255988575
3. Burde D. and Ceballos M., "Abelian ideals of maximal dimension for solvable Lie algebras", J. Lie Theory., 22 (2012), No. 3, 741-756. arXiv:0911.2995
4. Cairns G., Galić A.H. and Nikolayevsky Y., "Curvature properties of metric nilpotent Lie algebras which are independent of metric", Ann. Global Anal. Geom., 51 (2017), No. 3, 305-325. doi: 10.1007/s10455-016-9536-y
5. Gong M.P. "Classification of Nilpotent Lie algebras of Dimension 7 (Over Algebraically closed Fields and R)", Thesis (Ph.D.), University of Waterloo, Canada, 1998, 165 p.