Surface superconductivity and Hc3H_{c3} in UPt3_3

Surface superconductivity is studied within Ginzburg-Landau theory for two classes of models for the order parameter of UPt$_{3}$. The first class assumes two independent one-dimensional order parameters ($AB$ models), while the second assumes a single two-dimensional order parameter ($E$ models). $H_{c3}$ is calculated for all cases where the surface normal and magnetic field lie along high symmetry directions. Assuming specular reflection, it is found that except when ${\bf H}\parallel{\bf\hat c}$, the ratio $H_{c3}/H_{c2}$ is either unity or equals its `s-wave' value 1.695, although the precise $H_{c3}$ vs. $T$ curve predicted by the $AB$ and $E$ models differs for various geometries. The results are compared with recent experiments, and predictions are made for future experiments.Comment: 26 pages, with 6 figure

Singularities and normal forms of smooth distributions

In this expository paper we present main results (from classical to recent) on local classification of smooth distributions

Singularities and normal forms of generic 2-distributions on 3-manifolds

We give a complete classification of germs of generic 2-distributions on 3-manifolds. By a 2-distribution we mean either a module generated by two vector fields (at singular points its dimension decreases) or a Pfaff equation, i.e. a module generated by a differential 1-form (at singular points the dimension of its kernel increases)