English

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

Differential Geometry 2010-06-30 v1

Abstract

We study the volume growth of hyperkaehler manifolds of type AA_{\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 AA_{\infty} whose volume growth is r^a for each 3<a<4.

Keywords

Cite

@article{arxiv.1006.5504,
  title  = {The volume growth of hyperkaehler manifolds of type A_{\infty}},
  author = {Kota Hattori},
  journal= {arXiv preprint arXiv:1006.5504},
  year   = {2010}
}