11 citations · 23 across the 23 of their papers we have counts for
6 papers · 1 filter
Respectful decompositions of Lie algebras
Grant Cairns, Yuri Nikolayevsky
One of Pierre Molino's principal mathematical achievements was his theory of Riemannian foliations. One of his last papers, published in 2001, showed that his theory could be exten…
Curvature properties of metric nilpotent Lie algebras which are independent of metric
G. Cairns, A. Hinić Galić, Y. Nikolayevsky
This paper consists of two parts. First, motivated by classic results, we determine the subsets of a given nilpotent Lie algebra (respectively, of the Grassmannian o…
Geodesic Bases for Lie Algebras
Grant Cairns, Ana Hinić Galić, Yuri Nikolayevsky +1
For finite dimensional real Lie algebras, we investigate the existence of an inner product having a basis comprised of geodesic elements. We give several existence and non-existenc…
On the existence of orthonormal geodesic bases for Lie algebras
Grant Cairns, Nguyen Thanh Tung Le, Anthony Nielsen +1
We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand,…
Totally Geodesic Subalgebras of Filiform Nilpotent Lie algebras
Grant Cairns, Ana Hinić Galić, Yuri Nikolayevsky
We determine the maximal dimension of totally geodesic subalgebras of N-graded filiform Lie algebras, and we show that these bounds are attained.
Totally Geodesic Subalgebras of Nilpotent Lie algebras
Grant Cairns, Ana Hinić Galić, Yuri Nikolayevsky
A metric Lie algebra g is a Lie algebra equipped with an inner product. A subalgebra h of a metric Lie algebra g is said to be totally geodesic if the Lie subgroup corresponding to…