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arXiv · 1302.0776

Extremal Sasakian Geometry on S^3-bundles over Riemann Surfaces

Charles P. Boyer·Christina W. Tønnesen-Friedman
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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.

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BibTeXRIS

Charles P. Boyer, Christina W. Tønnesen-Friedman. 2013-02-04. Extremal Sasakian Geometry on S^3-bundles over Riemann Surfaces. https://arxiv.org/abs/1302.0776

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