Scalar flat Kähler metrics on affine bundles over CP1

Nobuhiro Honda

doi:10.3842/SIGMA.2014.046

Scalar flat Kähler metrics on affine bundles over CP¹

Nobuhiro Honda

SCI - Mathematics

Research output: Contribution to journal › Article

3 Citations (Scopus)

Abstract

We show that the total space of any affine C-bundle over CP¹ with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree.

Original language	English
Article number	046
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	10
DOIs	https://doi.org/10.3842/SIGMA.2014.046
Publication status	Published - 2014 Apr 19

Keywords

Affine bundle
Scalar-flat Kähler metric
Twistor space

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

Access to Document

10.3842/SIGMA.2014.046

Fingerprint Dive into the research topics of 'Scalar flat Kähler metrics on affine bundles over CP<sup>1</sup>'. Together they form a unique fingerprint.

Cite this

Honda, N. (2014). Scalar flat Kähler metrics on affine bundles over CP¹. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 10, [046]. https://doi.org/10.3842/SIGMA.2014.046

@article{ec07c964d05842f3889b7554ffe41dda,

title = "Scalar flat K{\"a}hler metrics on affine bundles over CP1",

abstract = "We show that the total space of any affine C-bundle over CP1 with negative degree admits an ALE scalar-flat K{\"a}hler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree.",

keywords = "Affine bundle, Scalar-flat K{\"a}hler metric, Twistor space",

author = "Nobuhiro Honda",

year = "2014",

month = apr,

day = "19",

doi = "10.3842/SIGMA.2014.046",

language = "English",

volume = "10",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - Scalar flat Kähler metrics on affine bundles over CP1

AU - Honda, Nobuhiro

PY - 2014/4/19

Y1 - 2014/4/19

N2 - We show that the total space of any affine C-bundle over CP1 with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree.

AB - We show that the total space of any affine C-bundle over CP1 with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree.

KW - Affine bundle

KW - Scalar-flat Kähler metric

KW - Twistor space

UR - http://www.scopus.com/inward/record.url?scp=84899149432&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899149432&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2014.046

DO - 10.3842/SIGMA.2014.046

M3 - Article

AN - SCOPUS:84899149432

VL - 10

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 046

ER -