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Correspondances géodésiques entre les surfaces euclidiennes à singularités coniques.

Mohammed Mostefa Mesmoudi (1996)

Revista Matemática Iberoamericana

A. J. Montesinos has shown that a geodesic correspondence between two complete Riemannian manifolds with transitive topological geodesic flow is a homothety. In this paper we prove a similar result for a conformal geodesic correspondence between two singular flat surfaces with conical singularities and negative concentrated curvature.

Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki (2012)

Annales Polonici Mathematici

It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation G . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing C r diffeomorphism group G is simple iff the foliation [ G , G ] defined by [G,G] admits no proper minimal sets....

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