Embeddings in Cp-spaces

Embeddings of polar spaces

In this article, two different notions of embeddings of polar spaces are compared. By using existing results in the field, a statement for a Fundamental Theorem of Polar Geometry is then obtained.

Embeddings of Real Projective Spaces

The question of finding the smallest Euclidean space in which real projective space P n can be (differentiably) embedded was the subject of intense investigation during the 1960s and 1970s. The purpose of this paper is to survey the status of the question, and add a little bit to our knowledge by proving one new family of embeddings, using old methods of obstruction theory. Our new result is gi...

Geometric embeddings of metric spaces

Embeddings of Affine Grassmann Spaces

In this paper we prove that if a Grassmann space Δ = GrA(m,h,K) of the h–subspaces of an affine space A = AG(m,K) has an embedding e into a projective space PG(n,K′) over a skew–field K′, and e satisfies two suitable conditions (α) and (β), then K and K′ are isomorphic fields and Δ is, up to projections, an affine Grassmannian. Mathematics Subject Classification (2000). 51A45; 51M35.

Affine Embeddings of Homogeneous Spaces

Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneous space G/H admits an affine embedding if and only if G/H is a quasi-affine algebraic variety. We start with some basic properties of affine embeddings and consider the cases, where the theory is well-de...