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An elementary proof of a Lima's theorem for surfaces.

Francisco Javier Turiel Sandín (1989)

Publicacions Matemàtiques

An elementary proof of the following theorem is given:THEOREM. Let M be a compact connected surface without boundary. Consider a C∞ action of Rn on M. Then, if the Euler-Poincaré characteristic of M is non zero there exists a fixed point.

Equivalence of control systems with linear systems on Lie groups and homogeneous spaces

Philippe Jouan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only if the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field is obtained by adding a left invariant one. Its projection on a homogeneous space, whenever it exists,...

Foliations of M 3 defined by 2 -actions

Jose Luis Arraut, Marcos Craizer (1995)

Annales de l'institut Fourier

In this paper we give a geometric characterization of the 2-dimensional foliations on compact orientable 3-manifolds defined by a locally free smooth action of 2 .

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