5 problems

CR transversality and nonvanishing Jacobian conjecture. The following are equivalent:

Let $V$ be a non-singular real projective surface, and let ${\mathbb R}V$ and ${\mathbb C}V$ denote its real and complex points. Write…

Classification conjecture. $M$ is Hopf and all its principal curvatures are constant if and only if $M$ is locally congruent to one of the examples $A_{+}$, $A_{-}$, $B_0$, $B_{+}$…

Let $M$ be a 3-dimensional connected real-analytic CR-manifold of hypersurface type, locally embedded in ${\mathbb C}^2$, and let $\mathop{\mathfrak {hol}}\nolimits(M,p)$ denote th…

Let $M$ be a real hypersurface in $SU_{2,m}/S(U_2U_m)$ whose principal curvatures satisfy the exceptional conditions in case (iv) of the main classification theorem: its normal bun…