Add to ORKGAbstract. We introduce a geometric invariant that we call the index of sym-metry, which measures how far is a Riemannian manifold from being a sym-metric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symme-try turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold. 1
We present a new method for classifying naturally reductive homogeneous spaces – i.e.homogeneous Rie...
Abstract. Let X = G/K be a Riemannian symmetric space of non-compact type and of rank ≥ 2. An irredu...
We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides wit...
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a R...
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a R...
By a recent result, it is known that compact homogeneous spaces with co-index of symmetry 4 are quot...
summary:Flag manifolds are in general not symmetric spaces. But they are provided with a structure o...
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z^k_2...
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z^k_2...
Given a compact Lie group G with Lie algebra gg, we consider its tangent Lie group TG≅G⋉AdgTG. In th...
The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic su...
In 1980, Oniˇsˇcik ([23]) introduced the index of a Riemannian symmetricspace as the minimal codimen...
Abstract. Let M be an irreducible Riemannian symmetric space. The index of M is the minimal codimens...
These notes cover the basics of Riemannian geometry, Lie groups, and symmetric spaces. This is just ...
We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove ...
We present a new method for classifying naturally reductive homogeneous spaces – i.e.homogeneous Rie...
Abstract. Let X = G/K be a Riemannian symmetric space of non-compact type and of rank ≥ 2. An irredu...
We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides wit...
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a R...
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a R...
By a recent result, it is known that compact homogeneous spaces with co-index of symmetry 4 are quot...
summary:Flag manifolds are in general not symmetric spaces. But they are provided with a structure o...
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z^k_2...
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z^k_2...
Given a compact Lie group G with Lie algebra gg, we consider its tangent Lie group TG≅G⋉AdgTG. In th...
The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic su...
In 1980, Oniˇsˇcik ([23]) introduced the index of a Riemannian symmetricspace as the minimal codimen...
Abstract. Let M be an irreducible Riemannian symmetric space. The index of M is the minimal codimens...
These notes cover the basics of Riemannian geometry, Lie groups, and symmetric spaces. This is just ...
We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove ...
We present a new method for classifying naturally reductive homogeneous spaces – i.e.homogeneous Rie...
Abstract. Let X = G/K be a Riemannian symmetric space of non-compact type and of rank ≥ 2. An irredu...
We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides wit...