Foliations with unbounded deviation on T 2 Dmitri Panov

نویسنده

  • Dmitri Panov
چکیده

This foliation is nonorientable and it has a transversal measure. The measure can be given locally out of the singularities by a closed 1-form. Half translation surfaces. Let M be a two-dimensional surface with a flat metric which has only conical singularities. The surface is called a half translation if the holonomy along any path on the surface is either Id or -Id. It is clear that the angles around the conical points should be an integer multiple of π. The surface is called a translation if the holonomy is always Id. A half translation structure gives rise to a family of foliations on the surface parametrized by the circle S. To construct a foliation from this family fix a tangent vector on the surface and move it to all the points of the surface by means of parallel translation. Since the holonomy is ±Id we obtain a foliation. A half translation surface can have only a finite group of automorphisms (with the only one exception of a flat torus). But if we forget about the metric and remember only the underlying affine structure on the surface we can have an interesting group of automorphisms preserving affine structure. The idea of the proof of the theorem 1 is the following. We construct a half translation torus with 3 singular points such that the underlying affine

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تاریخ انتشار 2008