Weakly complex homogeneous spaces

On Complex Weakly Commutative Homogeneous Spaces

Let G be a complex algebraic group and L an algebraic subgroup of G. The quotient space G/L is called weakly commutative if a generic orbit of the action G : T ∗(G/L) is a coisotropic submanifold. We classify weakly commutative homogeneous spaces N L/L in the case where L is a reductive group and the natural representation L : n/[n, n], where n is the tangent algebra of the group N , is

Nonlinear Bound States on Weakly Homogeneous Spaces

We prove the existence of ground state solutions for a class of nonlinear elliptic equations, arising in the production of standing wave solutions to an associated family of nonlinear Schrödinger equations. We examine two constrained minimization problems, which give rise to such solutions. One yields what we call Fλ-minimizers, the other energy minimizers. We produce such ground state solution...

Homogeneous Hypersurfaces in Complex Hyperbolic Spaces

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.

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