标题： 关于具有最多共形 Killing 向量的空间 显示英文标题

标题： On Spaces with the Maximal Number of Conformal Killing Vectors

摘要： 自然可以预期并很容易证明，每个共形平坦空间都具有最大数量的共形 Killing 向量场（CKVs）。 另一方面，有趣的是询问其逆命题是否成立。 共形平坦性是存在最大数量 CKVs 的必要条件吗？ 在本文综述中证明了答案是肯定的，当且仅当空间是共形平坦时，它才具有最大数量的 CKVs。 显示英文摘要

摘要： It is natural to expect and simple to prove that every conformally flat space possess the maximal number of conformal Killing vector fields (CKVs). On the other hand, it is interesting to ask whether the converse is true. Is conformal flatness a necessary condition for the existence of the maximal number of CKVs? In this review article it is proven that the answer is yes, a space admits the maximal number of CKVs if, and only if, it is conformally flat.