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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 046, 25 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.046 (Mi sigma911) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Scalar Flat Kähler Metrics on Affine Bundles over $\mathbb{CP}^1$

Nobuhiro Honda

Mathematical Institute, Tohoku University, Sendai, Miyagi, Japan
Full-text PDF (471 kB) Citations (4)
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DOI: https://doi.org/10.3842/SIGMA.2014.046
Abstract: We show that the total space of any affine $\mathbb{C}$-bundle over $\mathbb{CP}^1$ 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.
Keywords: scalar-flat Kähler metric; affine bundle; twistor space.
Received: November 12, 2013; in final form April 15, 2014; Published online April 19, 2014
Bibliographic databases:
Document Type: Article
MSC: 53A30
Language: English
Citation: Nobuhiro Honda, “Scalar Flat Kähler Metrics on Affine Bundles over $\mathbb{CP}^1$”, SIGMA, 10 (2014), 046, 25 pp.
Citation in format AMSBIB
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\by Nobuhiro~Honda
\paper Scalar Flat K\"ahler Metrics on Affine Bundles over $\mathbb{CP}^1$
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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