More on the Determinacy of Smooth Map-Germs.
It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.
We compute the global multiplicity of a 1-dimensional foliation along an integral curve in projective spaces. We give a bound in the way of Poincaré problem for a complete intersection curves. In the projective plane, this bound give us a bound of the degree of non irreducible integral curves in function of the degree of the foliation.
Let be a -dimensional foliation on an -manifold , and the -tangent bundle of . The purpose of this paper is to present some reltionship between the foliation and a natural lifting of to the bundle . Let
A classification of natural liftings of foliations to the tangent bundle is given.