Nash G manifold structures of compact or compactifiable C∞G manifolds

Definable C∞g Manifold Structures of Definable Cg Manifolds

Let G be a compact definable C∞ group and 2 ≤ r < ∞. Let X be a noncompact affine definable CG manifold and X1, . . . , Xk noncompact codimension one definable CG submanifolds of X such that X1, . . . , Xk are in general position in X and (X;X1, . . . , Xk) satisfies the frontier condition. We prove that (X;X1, . . . , Xk) admits a unique definable C∞G manifold structure (Y ;Y1, . . . , Yk).

Locally definable C∞G manifold structures of locally definable CG manifolds

zw Let G be a finite abelian group and 1 ≤ r < ∞. We prove that every locally definable CG manifold admits a unique locally definable C∞G manifold structure up to locally definable C∞G diffeomorphism. zh 2000 Mathematics Subject Classification. 14P10, 14P20, 57S05, 57S15, 58A05, 58A07, 03C64.

Normal Cr Structures on Compact 3-manifolds

We study normal CR compact manifolds in dimension 3. For a choice of a CR Reeb vector field, we associate a Sasakian metric on them, and we classify those metrics. As a consequence, the underlying manifolds are topologically finite quotiens of S or of a circle bundle over a Riemann surface of positive genus. In the latter case, we prove that their CR automorphisms group is a finite extension of...

A Note on Exponentially Nash G Manifolds and Vector Bundles

Global Structures on CR Manifolds via Nash Blow-ups

A generic compact real codimension two submanifold X of Cn+2 will have a CR structure at all but a finite number of points (failing at the complex jump points J). The main theorem of this paper gives a method of extending the CR structure on the non-jump points X − J to the jump points. We examine a Gauss map from X − J to an appropriate flag manifold F and take the closure of the graph of this...