The volume growth of hyperkaehler manifolds of type A_{\infty}

Details The volume growth of hyperkaehler manifolds of type A_{\infty} The volume growth of hyperkaehler manifolds of type A_{\infty}

2010-06-29

arxiv.org/abs/1006.5504v1

Mathematics

Differential Geometry

Scientific paper

We study the volume growth of hyperkaehler manifolds of type $A_{\infty}$ constructed by Anderson-Kronheimer-LeBrun and Goto. These are noncompact complete 4-dimensional hyperkaehler manifolds of infinite topological type. These manifolds have the same topology but the hyperkaehler metrics are depends on the choice of parameters. By taking a certain parameter, we show that there exists a hyperkaehler manifold of type $A_{\infty}$ whose volume growth is r^a for each 3

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