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Morse index of a cyclic polygon

Gaiane Panina, Alena Zhukova (2011)

Open Mathematics

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.

Multiplicity of a foliation on projective spaces along an integral curve.

Julio García (1993)

Revista Matemática de la Universidad Complutense de Madrid

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.

Natural liftings of foliations to the r -tangent bunde

Mikulski, Włodzimierz M. (1994)

Proceedings of the Winter School "Geometry and Physics"

Let F be a p -dimensional foliation on an n -manifold M , and T r M the r -tangent bundle of M . The purpose of this paper is to present some reltionship between the foliation F and a natural lifting of F to the bundle T r M . Let L q r ( F ) ( q = 0 ,...

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