On the realization of Riemannian symmetric spaces in Lie groups

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G.     

On the realization of Riemannian symmetric spaces in Lie groups II

In this paper we generalize a result in [J. An, Z. Wang, On the realization of Riemannian symmetric spaces in Lie groups, Topology Appl. 153 (7) (2005) 1008-1015, showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of fixed points of involutions are also proved.     

Estimates of orders of groups of projective transformations of Riemannian spaces

Translated from Matematicheskie Zametki, Vol. 43, No. 2, pp. 256–262, February, 1988.     

H-transformations in Riemannian spaces

A Riemannian space V_n (n = mr), equipped with an integrable regular H-structure isomorphic to a hypercomplex algebra h (dim h = r), is considered as a real realization of a hypercomplex manifold over the algebra h. The geometry of can be mapped into the geometry of V_n. In particular, with the transformations of are associated H transformations (preserving the H-structure of the space) in V_n. The H-conformal and the H-projective transformations of Vn are investigated.Translated from Matematicheskie Zametki, Vol. 23, No. 4, pp. 617–625, April, 1978.     

Semi-classical analysis on H-type groups

Science China Mathematics - In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodi fferential operators, prove the boundedness of their action on...     

Jordan triples and Riemannian symmetric spaces

We introduce a class of real Jordan triple systems, called JH-triples, and show, via the Tits-Kantor-Koecher construction of Lie algebras, that they correspond to a class of Riemannian symmetric spaces including the Hermitian symmetric spaces and the symmetric R-spaces.     

Transformations in hypercomplex Riemannian spaces

It is well known that an integrable regular H-structure induces on a real manifold M_n the structure of a hypercomplex analytic manifold (h-manifold) \(\mathop M\limits^* _m \) . We prove that the Lie derivative of a pure tensor T on M_n is an h-derivative of Lie providing T is h-analytic. With the h-derivative of Lie there is associated on \(\mathop M\limits^* _m \) the hypercomplex derivative of Lie. This enables us to associate to the motions and affine collineations in the Riemannian space \(\mathop V\limits^* _m \) corresponding transformations in a real space V_n.     

The heat kernel on H-type groups

In this paper we present an explicit calculation of the heat kernel for the sub-Laplacian on an H-type group by using irreducible unitary representations of and the heat kernel for the associated Hermite operator.

     

Ostrowski type inequalities on H-type groups

The main aim of this paper is to establish an Ostrowski type inequality on H-type groups using the L^∞ norm of the horizontal gradient. The work has been motivated by the work of Anastassiou and Goldstein in [G.A. Anastassiou, J.A. Goldstein, Higher order Ostrowski type inequalities over Euclidean domains, J. Math. Anal. Appl. 337 (2008) 962-968].     

Spaces and moduli spaces of Riemannian metrics

These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness properties. They also discuss several open problems and questions in the field.     

Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces

In this paper we define a distinguished boundary for the complex crowns of non-compact Riemannian symmetric spaces . The basic result is that affine symmetric spaces of can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.