2014/04/24 by Isaev, Alexander
#32V05 #32V40 #53A15 #53C24 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1404.6148
Let C(2,1) be the class of connected 5-dimensional CR-hypersurfaces that are 2-nondegenerate and uniformly Levi degenerate of rank 1. In a recent article, we proved that the CR-structures in C(2,1) are reducible to so(3,2)-valued absolute parallelisms. In the present paper, we apply this result to study tube hypersurfaces in C3 that belong to C(2,1) and whose CR-curvature identically vanishes. Every such hypersurface is shown to be affinely equivalent to an open subset of the tube over the future light cone.