We develop a general theory for irreducible homogeneous spaces M= G/H, in relation to the
nullity distribution ν of their curvature tensor. We construct natural invariant (different and …

We find new conditions that the existence of nullity of the curvature tensor of an irreducible
homogeneous space $ M= G/H $ imposes on the Lie algebra $\mathfrak g $ of $ G $ and on …

We develop a general structure theory for compact homogeneous Riemannian manifolds in
relation to the coindex of symmetry. We will then use these results to classify irreducible …

Riemannian geodesic orbit spaces (G/H, g) are natural generalizations of symmetric spaces,
defined by the property that their geodesics are orbits of one-parameter subgroups of G. We …

We compute the full isometry group of any left-invariant metric on a simply connected, non-
unimodular Lie group of dimension three. As an application, we determine the index of …

We show that a tensor product of four specific $1 {+} 2$ Minkowski vacuum states is a self-
consistent vacuum state for an infinite set of three-dimensional anti-de Sitter (AdS $ _3 $) …

We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-
invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group …

The sedenion algebra $\mathbb S $ is a non-commutative, non-associative, $16 $-
dimensional real algebra with zero divisors. It is obtained from the octonions through the …

Naturally reductive spaces are studied with the aim to classify them. The in this thesis
developed theory contains a construction which produces many unknown non-normal …

We study the index of symmetry of a compact generalized flag manifold M= G/H endowed
with an invariant Kähler structure. When the group G is simple we show that the leaves of …