Invariants and Umbilical Points on Three Dimensional CR Manifolds embedded in ${\mathbb{C}}^2$

Abstract

We introduce a new sequence of CR invariant determinants on a three dimensional CR manifold $M$ embedded in ${\mathbb{C}}^2$. The lowest order invariant $\det A_3$ represents E. Cartan's 6th order invariant (the umbilical "tensor"), whose zero locus yields the set of umbilical points on $M$. As an application of this new presentation of the umbilical invariant, we show that generic, almost circular perturbations of the unit sphere always contain curves or surfaces of umbilical points.

Cited by in corpus (1)

• Bounded strictly pseudoconvex domains in ${\mathbb{C}}^2$ with obstruction flat boundary