The Pick cubic form is a fundamental invariant in the (equi)affine differential geometry of hypersurfaces. We study its role in the affine isometric embedding problem, using exterior differential systems (EDS). We give pointwise conditions on the Pick form under which an isometric embedding of a Riemannian manifold M3 into R4 is rigid. The role of the Pick form in the characteristic variety of ...

In this paper, we derive a new fast algorithm for the matrixvalued Nevanlinna-Pick interpolation. Given n distinct points zi in the unit disk jzj < 1 and n complex matrices Wk of dimension m m, satisfying the Pick condition for 1 k n, the new Nevanlinna-Pick interpolation algorithm requires only 20 3 nm 3 complex arithmetic operations to evaluate the matrix-valued interpolatory rational functio...