Spherical Tube Hypersurfaces
We believe Levi non-degenerate tube hypersurfaces in complicated linear house which might be "round", this is, in the community CR-equivalent to the actual hyperquadric. Spherical hypersurfaces are characterised through the situation of the vanishing of the CR-curvature shape, so such hypersurfaces are flat from the CR-geometric point of view. On the opposite hand, such hypersurfaces are of passion from the viewpoint of affine geometry. Thus our remedy of round tube hypersurfaces on this e book is two-fold: CR-geometric and affine-geometric. Spherical tube hypersurfaces end up to own outstanding homes. For instance, each such hypersurface is real-analytic and extends to a closed real-analytic round tube hypersurface in complicated house. One of our major objectives is to provide an particular affine classification of closed round tube hypersurfaces each time conceivable. In this e book we provide a complete exposition of the speculation of round tube hypersurfaces beginning with the theory proposed within the pioneering paintings through P. Yang (1982) and finishing with the brand new method because of G. Fels and W. Kaup (2009).