标题： 叶状循环在复流形上的自交 显示英文标题

标题： Self-intersection of foliated cycles on complex manifolds

摘要： 设X为一个紧致的Kahler流形，T是由X上的横截Lipschitz层结构所引导的叶状循环。我们证明了只要T不包含沿紧致流形的积分电流，T的上同调类的自交集就为零。作为推论，我们证明了在某些流形（例如射影空间）中，低余维的横截Lipschitz层结构除了沿紧致叶的积分给出的叶状循环外，不携带任何其他的叶状循环。 显示英文摘要

摘要： Let X be a compact Kahler manifold and let T be a foliated cycle directed by a transversally Lipschitz lamination on X . We prove that the self-intersection of the cohomology class of T vanishes as long as T does not contain currents of integration along compact manifolds. As a consequence we prove that transversally Lipschitz laminations of low codimension in certain manifolds, e.g. projective spaces, do not carry any foliated cycles except those given by integration along compact leaves.