Invariant scalar-flat Kähler metrics on \(\mathcal {O} (- \ell )\)
type: Item
instance of: scholarly article
title: Invariant scalar-flat Kähler metrics on \(\mathcal {O} (- \ell )\)
zbMATH Open document ID: 1422.53060
author: Paul Gauduchon
published in: Bollettino dell'Unione Matematica Italiana
publication date: 2019-06-27T00:00:00Z
review text: The author studies several extremal Kähler metrics, in a unified framework based on the momentum profile by \textit{A. D. Hwang} and \textit{M. A. Singer} [Trans. Am. Math. Soc. 354, No. 6, 2285--2325 (2002; Zbl 0987.53032)]. In the first part, the author focuses on $\mathrm{U}(m)$-invariant scalar-flat Kähler metrics on $\mathcal{O}(-\ell)$ over $\mathbb{P}^{m-1}$, which include the Burns-Simanca metrics, see [\textit{D. Burns}, Twistors and harmonic maps. AMS conference talk (unpublished) (1986); \textit{S. R. Simanca}, Math. Ann. 291, No. 2, 239--246 (1992; Zbl 0725.53066)], and \textit{C. LeBrun}'s metrics, see [Commun. Math. Phys. 118, No. 4, 591--596 (1988; Zbl 0659.53050)]. Then, he also considers the extremal Kähler metrics on ruled manifolds over $\mathbb P^{m-1}$ by \textit{E. Calabi} [Ann. Math. Stud. 102, 259--290 (1982; Zbl 0487.53057)].
reviewed by: Daniele Angella
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 7074512
zbMATH Keywords: extremal Kähler metrics
zbMATH Keywords: toric manifolds
zbMATH Keywords: momentum profile
zbMATH Keywords: mass
MaRDI profile type: Publication
full work available at URL: s40574-018-0179-8
OpenAlex ID: W2898970774
Wikidata QID: Q126097423
cites work: KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS
cites work: Q4803675
cites work: Hamiltonian 2-forms in Kähler geometry. III: Extremal metrics and stability
cites work: Blowing up and desingularizing constant scalar curvature Kähler manifolds
cites work: Blowing up Kähler manifolds with constant scalar curvature. II.
cites work: Extremal metrics on blowups
cites work: Q4720334
cites work: Métriques kählériennes et fibrés holomorphes
cites work: Q3948283
cites work: Q3694298
cites work: On conformally Kähler, Einstein manifolds
cites work: Q3041921
cites work: Kahler geometry on toric manifolds, and some other manifolds with large symmetry
cites work: Kaehler structures on toric varieties
cites work: Moment maps and combinatorial invariants of Hamiltonian \(T^ n\)-spaces
cites work: Mass in Kähler geometry
cites work: A momentum construction for circle-invariant Kähler metrics
cites work: Counter-examples to the generalized positive action conjecture
cites work: Einstein Metrics on Complex Surfaces
cites work: On Einstein, Hermitian 4-manifolds
cites work: Einstein manifolds and extremal Kähler metrics
cites work: Kähler metrics of constant scalar curvature on bundles over \({\mathbb{C}}{\mathbb{P}}_{n-1}\)
cites work: Q5169932
DOI: 10.1007/S40574-018-0179-8
description: scientific article; zbMATH DE number 7074512