Abstract
We study the volume growth of hyper-Kähler manifolds of type A ∞ constructed by Anderson-Kronheimer-LeBrun (Commun. Math. Phys. 125:637-642, 1989) and Goto (Geom. Funct. Anal. 4(4):424-454, 1994). These are noncompact complete 4-dimensional hyper-Kähler manifolds of infinite topological type. These manifolds have the same topology, but the hyper-Kähler metrics depend on the choice of parameters. By taking a certain parameter, we show that there exists a hyper-Kähler manifold of type A ∞ whose volume growth is r α for each 3<α<4.
Original language | English |
---|---|
Pages (from-to) | 920-949 |
Number of pages | 30 |
Journal | Journal of Geometric Analysis |
Volume | 21 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2011 Oct 1 |
Externally published | Yes |
Keywords
- Gibbons-Hawking ansatz
- Hyper-Kähler quotient
- Volume growth
ASJC Scopus subject areas
- Geometry and Topology