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 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 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}
}