Automorphisms of Locally Conformally Kahler Manifolds

作者：Ornea Liviu^*; Verbitsky Misha

来源：International Mathematics Research Notices, 2012, 2012(4): 894-903.

DOI：10.1093/imrn/rnr053

A manifold M is locally conformally Kahler (LCK), if it admits a Kahler covering (M) over tilde with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure gives a G-invariant LCK metric. Suppose that S1 acts on an LCK manifold M by holomorphic isometries, and the lifting of this action to the Kahler cover (M) over tilde is not isometric. We show that (M) over tilde admits an automorphic Kahler potential, and hence (for dimC M %26gt; 2) the manifold M can be embedded to a Hopf manifold.

• 出版日期2012