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...

A design is a finite set of points in a space on which every ”simple” functions averages to its global mean. Illustrative examples of simple functions are low-degree polynomials on the Euclidean sphere or on the Hamming cube. We prove lower bounds on designs in spaces with a large group of symmetries. These spaces include globally symmetric Riemannian spaces (of any rank) and commutative associ...

Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

In this paper, the reflection of ultrasonic guided waves from simple dent in pipes has been investigated using finite element method and the relationship between reflection coefficient of these waves and deformation rate has been determined. Also, the effect of the parameters of wave generation source on the generated wave field has been investigated using normal modes expansion method. At firs...

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...

In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. By virtue of the properties of Γ-convex and KC-map, we give some sufficient conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. As application, we show an existence theorem of...

We study the canonical complexifications of non-compact Riemannian symmetric spaces by the Grauert tube construction. We determine the maximal such complexification, a domain already constructed by Akhiezer and Gindikin [1], and show that this domain is Stein. We also determine when invariant complexifications, including the maximal one, are Hermitian symmetric. This is expressed simply in term...

(2) the product H × H of 2 hyperbolic planes. In short, among all the symmetric spaces of noncompact type with rank ≥ 2, there are only two manifolds that are minimal with respect to the partial order defined by totally geodesic embeddings. Our main theorem provides an analogue of this result for noncompact finitevolume spaces that are locally symmetric, rather than globally symmetric, but, in ...