Some recent developments in the theory of properly embedded minimal surfaces in
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 .
The first part of this paper is concerned with geometrical and cohomological properties of Lie flows on compact manifolds. Relations between these properties and the Euler class of the flow are given.The second part deals with 3-codimensional Lie flows. Using the classification of 3-dimensional Lie algebras we give cohomological obstructions for a compact manifold admits a Lie flow transversely modeled on a given Lie algebra.
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.
Nearly-quaternionic Kähler manifolds of dimension at least are shown to be quaternionic Kähler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic Kähler are also found.
In this note, we are concerned with the Kozlowski-Simon conjecture on ovaloids and prove that it is correct under additional conditions.