论文标题
非线性HOPF歧管是本地合成的Kahler
Non-linear Hopf manifolds are locally conformally Kahler
论文作者
论文摘要
HOPF歧管是由全体形态收缩生成的环状组的$ C^n \ Backslash 0 $的商。 Hopf歧管是差异到$ s^1 \ times s^{2n-1} $，因此不接受Kahler指标。众所周知，由线性收缩（称为线性HOPF歧管）定义的HOPF歧管具有局部合并的Kahler（LCK）指标。在本文中，我们证明，由非线性全体形态收缩定义的HOPF流形将霍明型嵌入到线性Hopf歧管中，此外，它们承认LCK指标。
A Hopf manifold is a quotient of $C^n\backslash 0$ by the cyclic group generated by a holomorphic contraction. Hopf manifolds are diffeomorphic to $S^1\times S^{2n-1}$ and hence do not admit Kahler metrics. It is known that Hopf manifolds defined by linear contractions (called linear Hopf manifolds) have locally conformally Kahler (LCK) metrics. In this paper we prove that the Hopf manifolds defined by non-linear holomorphic contractions admit holomorphic embeddings into linear Hopf manifolds, and, moreover they admit LCK metrics.
