Extremal Sasakian geometry on \(S^{3}\)-bundles over Riemann surfaces
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Publication:2929651
DOI10.1093/IMRN/RNT139zbMATH Open1307.53036arXiv1302.0776OpenAlexW2169971338MaRDI QIDQ2929651
Author name not available (Why is that?)
Publication date: 14 November 2014
Published in: (Search for Journal in Brave)
Abstract: In this paper we study the Sasakian geometry on S^3-bundles over a Riemann surface of genus g>0 with emphasis on extremal Sasaki metrics. We prove the existence of a countably infinite number of inequivalent contact structures on the total space of such bundles that admit 2-dimensional Sasaki cones each with a Sasaki metric of constant scalar curvature (CSC). This CSC Sasaki metric is most often irregular. We further study the extremal subset in the Sasaki cone showing that if 0<g<5 it exhausts the entire cone. Examples are given where exhaustion fails.
Full work available at URL: https://arxiv.org/abs/1302.0776
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