Reflector spaces over the 4-dimensional Kaneyuki-Kozai's para-Hermitian symmetric spaces.
The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for -graded parabolic geometries and for almost Grassmannian structures, in particular. As an application of two general constructions with parabolic geometries, we present an example of non-flat Grassmannian symmetric space. Next we observe there is a distinguished torsion-free...
We consider symmetries on filtered manifolds and we study the -graded parabolic geometries in more details. We discuss the existence of symmetries on the homogeneous models and we conclude some simple observations on the general curved geometries.
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of -symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. The conditions for a metric adapted to the -symmetric structure to be naturally reductive are detailed for the flag manifold .
We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.
Soit une algèbre de Jordan simple euclidienne de dimension finie et le cône symétrique associé. Nous étudions dans cet article le semi-groupe , naturellement associé à , formé des automorphismes holomorphes du domaine tube qui appliquent le cône dans lui-même.
We determine explicitly the local structure of a semi-symmetric -space.