English

Zero CR-curvature equations for Levi degenerate hypersurfaces via Pocchiola's invariants

Complex Variables 2018-09-24 v1 Differential Geometry

Abstract

In our earlier articles we studied tube hypersurfaces in C3{\mathbb C}^3 that are 2-nondegenerate and uniformly Levi degenerate of rank 1. In particular, we showed that the vanishing of the CR-curvature of such a hypersurface is equivalent to the Monge equation with respect to one of the variables. In the present paper we provide an alternative shorter derivation of this equation by utilizing two invariants discovered by S. Pocchiola. We also investigate Pocchiola's invariants in the rigid case and give a partial classification of rigid 2-nondegenerate uniformly Levi degenerate of rank 1 hypersurfaces with vanishing CR-curvature.

Keywords

Cite

@article{arxiv.1809.03029,
  title  = {Zero CR-curvature equations for Levi degenerate hypersurfaces via Pocchiola's invariants},
  author = {Alexander Isaev},
  journal= {arXiv preprint arXiv:1809.03029},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1608.02919