Extremal Sasakian geometry on \(S^{3}\)-bundles over Riemann surfaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 1307.53036
author: Charles P. Boyer
author: Christina W. Tønnesen-Friedman
publication date: 2014-11-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1302.0776
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 6369440
zbMATH Keywords: extremal Sasaki metrics
zbMATH Keywords: constant scalar curvature
zbMATH Keywords: Sasaki cone
MaRDI profile type: Publication
OpenAlex ID: W2169971338
arXiv ID: 1302.0776
DOI: 10.1093/IMRN/RNT139
published in: IMRN. International Mathematics Research Notices
title: Extremal Sasakian geometry on \(S^{3}\)-bundles over Riemann surfaces
review text: As an extension of [the authors, Afr. Diaspora J. Math. 14, No. 2, 98--117 (2012; Zbl 1285.53034)], the authors investigate the existence of extremal Sasaki metrics on \(S^3\)-bundle, over a Riemann surface of genus \(g>0\). They prove the existence of a countably infinite number of inequivalent contact structures on the total space of the considered bundles, which admits 2D Sasaki cones, each with a Sasaki metrics of constant scalar curvature. Studying the extremal subset in the Sasaki cone, they obtain that it exhausts the entire cones, under the assumption \(0<g\leq4\).
reviewed by: Nicoleta Aldea
description: scientific article; zbMATH DE number 6369440