Curvature homogeneous spaces with a solvable Lie group as homogeneous model

Homogeneous Spaces Defined by Lie Group Automorphisms. Ii

We will drop the compactness hypothesis on G in the results of §6, doing this in such a way that problems can be reduced to the compact case. This involves the notions of reductive Lie groups and algebras and Cartan involutions. Let © be a Lie algebra. A subalgebra S c © is called a reductive subaU gebra if the representation ad%\® of ίΐ on © is fully reducible. © is called reductive if it is a...

On Riemannian Curvature of Homogeneous Spaces

Curvature homogeneous spaces whose curvature tensors have large symmetries

We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large” Lie subalgebras h of so(n). In this paper we deal with the cases of h = so(r)⊕ so(n− r) (2 ≤ r ≤ n− r), so(n− 2), and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces