曲面上的拟齐次解析仿射联络
Quasihomogeneous analytic affine connections on surfaces
摘要：
我们对紧定向实解析曲面上的无挠实解析仿射联络进行了分类，这些曲面在非平凡开集上是局部齐性的，而在所有曲面上不是局部齐性的。特别是，我们证明了这种联系的存在。这种分类依赖于一个本地的结果，分类芽的挠自由真正的解析仿射联络在附近的原点在平面上是quasihomogeneous，在这个意义上说，他们是本地齐次的开集包含在其封闭的原点，但不是本地齐次的原点附近。
英文摘要：
We classify torsion-free real-analytic affine connections on compact oriented real-analytic surfaces which are locally homogeneous on a nontrivial open set, without being locally homogeneous on all of the surface. In particular, we prove that such connections exist. This classification relies in a local result that classifies germs of torsion-free real-analytic affine connections on a neighborhood of the origin in the plane which are quasihomogeneous, in the sense that they are locally homogeneous on an open set containing the origin in its closure, but not locally homogeneous in the neighborhood of the origin.
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