Plane Curves Which are Quantum Homogeneous Spaces

Quantum Homogeneous Spaces as Quantum Quotient Spaces

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail. 0. Introduction A homogeneous space X of a Lie group G may be always identified wit...

Elliptic Curves on Some Homogeneous Spaces

Let X be a minuscule homogeneous space, an odddimensional quadric, or an adjoint homogenous space of type different from A and G2. Le C be an elliptic curve. In this paper, we prove that for d large enough, the scheme of degree d morphisms from C to X is irreducible, giving an explicit lower bound for d which is optimal in many cases. 2010 Mathematics Subject Classification: 14M15, 14N35

Riemannian Geometries on Spaces of Plane Curves

We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from S1 to the plane modulo the group of diffeomorphisms of S1, acting as reparametrizations. In particular we investigate the metric, for a constant A > 0, Gc (h, k) := ∫ S1 (1+ Aκc(θ) 2)〈h(θ), k(θ)〉|c(θ)| dθ where κc is the curvature of the curve c and h, k are normal vector ...

Bilipschitz Homogeneous Curves in R2 Are Quasicircles

Curvature Homogeneous Pseudo-riemannian Manifolds Which Are Not Locally Homogeneous

We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.