Metrics on spaces of immersions where horizontality equals normality

σ-Normality of Topological Spaces

Tight Equivariant Immersions of Symmetric Spaces

Introduction. Let G/K be a compact, irreducible symmetric space and Q = f+p the Lie algebra of G. If ir is a non trivial real class-one representation of G on E with O^e, infixed, then the map TlG/K —*E given by gK—*ir{g)e gives an immersion of G/K into E. The purpose of this note is to announce the classification of such immersions with minimal absolute curvature (i.e., are tight) [ l ] , [4]....

Hörmander’s Condition for Normal Bundles on Spaces of Immersions

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two subbundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes the sub-Riemannian geometries of these bundles. In particular, we show for a selection of bundles which naturally occur in applications that they are either b...

CR Singular Immersions of Complex Projective Spaces

Quadratically parametrized smooth maps from one complex projective space to another are constructed as projections of the Segre map of the complexification. A classification theorem relates equivalence classes of projections to congruence classes of matrix pencils. Maps from the 2-sphere to the complex projective plane, which generalize stereographic projection, and immersions of the complex pr...

Metrics on State Spaces

In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the metric they define on the state space, to the extreme points of the state space. We characterize the Lipschitz norms which are determined by their metric on the ...