论文标题
弯曲N体问题的普通中央配置的紧凑性和索引
Compactness and index of ordinary central configurations for the curved n-body problem
论文作者
论文摘要
对于弯曲的N体问题，我们表明，普通中央配置的集合远离H^3中的大多数奇异配置，并且远离S^3中的单数配置子集。我们还表明，n个质量的N！/2 GEODESIC普通中央构型都有Morse索引n-2。然后，如果这些质量的所有普通中心构型是非分类的，那么我们得到了一个直接的推论，至少有（3n-4）（N-4）（N-1）！/2普通的中心构型。
For the curved n-body problem, we show that the set of ordinary central configurations is away from most singular configurations in H^3, and away from a subset of singular configurations in S^3. We also show that each of the n!/2 geodesic ordinary central configurations for n masses has Morse index n-2. Then we get a direct corollary that there are at least (3n-4)(n-1)!/2 ordinary central configurations for given n masses if all ordinary central configurations of these masses are non-degenerate.
