Some Global Properties of Plane Curves
We determine all natural operators transforming vector fields on a manifold to vector fields on , , and all natural operators transforming vector fields on to functions on , . We describe some relations between these two kinds of natural operators.
In this paper we review some of the concepts and results of V. I. Arnol’d [1] for curves in and extend them to curves and surfaces in .
We consider graphs of positive scalar or Gauss-Kronecker curvature over a punctured disk in Euclidean and hyperbolic -dimensional space and we obtain removable singularities theorems.
In this note, we are concerned with the Kozlowski-Simon conjecture on ovaloids and prove that it is correct under additional conditions.
We focus our attention on projectively flat affine surfaces. First, we classify the affine surfaces with projectively flat induced connection and constant Pick invariant. We also investigate the compact case and study how the geometry at the boundary determines the geometry of the surface.