In this paper, new examples of weakly symmetric spaces in the sense of A. Selberg 14] are constructed. Let G be a connected, simply-connected, simple Lie group of hermitian type and K a maximal compactly embedded subgroup of G such that D = G=K is an irreducible classical bounded symmetric domain. Let G 1 and D 1 be circle extensions of G and D, respectively. The factor of automorphy induces a ...

Weakly symmetric spaces are particular Riemannian homogeneous spaces which have been introduced by Selberg [21] in 1956 in the framework of his trace formula. They attracted only little interest until the author and Vanhecke [7] found a simple geometric characterization of weakly symmetric spaces which lead to a large number of new examples. The purpose of this note is to present a survey about...

The object of the present paper is to study the totally umbilical hypersurfaces of weakly projective symmetric spaces and it is shown that the totally umbilical hypersurfaces of weakly projective symmetric space is also a weakly projective symmetric space.

Let K ⊂ G be a compact subgroup of a real Lie group G. Denote by D(X) thealgebra of G-invariant differential operators on the homogeneous space X = G/K. ThenX is called commutative or the pair (G,K) is called a Gelfand pair if the algebra D(X)is commutative. Symmetric Riemannian homogeneous spaces introduced by Élie Cartanand weakly symmetric homogeneous spaces introduced by Sel...

Symmetric spaces in the sense of E. Cartan supply major examples in Riemannian geometry. The study of their structure is connected closely to the theory of Lie groups. On these spaces, global analysis, particularly integration theory and theory of partial differential operators, arises in a canonical fashion by the requirement of geometric invariance. On R these two subjects are related to one ...

Let (G,H) be a spherical pair and assume that G is a connected compact simple Lie group and H a closed subgroup of G. We prove in this paper that the homogeneous manifold G/H is weakly symmetric with respect to G and possibly an additional fixed isometry μ. It follows that M. Krämer’s classification list of such spherical pairs also becomes a classification list of compact weakly symmetric spac...