The volume growth of hyper-Kähler manifolds of type A ∞

Kota Hattori

doi:10.1007/s12220-010-9173-9

The volume growth of hyper-Kähler manifolds of type A _∞

Kota Hattori

Research output: Contribution to journal › Article

6 Citations (Scopus)

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	https://doi.org/10.1007/s12220-010-9173-9
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

Access to Document

10.1007/s12220-010-9173-9

Fingerprint Dive into the research topics of 'The volume growth of hyper-Kähler manifolds of type A <sub>∞</sub>'. Together they form a unique fingerprint.

Cite this

Hattori, K. (2011). The volume growth of hyper-Kähler manifolds of type A _∞. Journal of Geometric Analysis, 21(4), 920-949. https://doi.org/10.1007/s12220-010-9173-9

@article{61ae0f0c3ac54673abc782a185689994,

title = "The volume growth of hyper-K{\"a}hler manifolds of type A ∞",

abstract = "We study the volume growth of hyper-K{\"a}hler 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-K{\"a}hler manifolds of infinite topological type. These manifolds have the same topology, but the hyper-K{\"a}hler metrics depend on the choice of parameters. By taking a certain parameter, we show that there exists a hyper-K{\"a}hler manifold of type A ∞ whose volume growth is r α for each 3<α<4.",

keywords = "Gibbons-Hawking ansatz, Hyper-K{\"a}hler quotient, Volume growth",

author = "Kota Hattori",

year = "2011",

month = oct,

day = "1",

doi = "10.1007/s12220-010-9173-9",

language = "English",

volume = "21",

pages = "920--949",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - The volume growth of hyper-Kähler manifolds of type A ∞

AU - Hattori, Kota

PY - 2011/10/1

Y1 - 2011/10/1

N2 - 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.

AB - 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.

KW - Gibbons-Hawking ansatz

KW - Hyper-Kähler quotient

KW - Volume growth

UR - http://www.scopus.com/inward/record.url?scp=80053053193&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053053193&partnerID=8YFLogxK

U2 - 10.1007/s12220-010-9173-9

DO - 10.1007/s12220-010-9173-9

M3 - Article

AN - SCOPUS:80053053193

VL - 21

SP - 920

EP - 949

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 4

ER -