Canonical Sasakian metrics
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Publication:926256
DOI10.1007/S00220-008-0429-1zbMATH Open1142.53036arXivmath/0604325OpenAlexW2075601138MaRDI QIDQ926256
Author name not available (Why is that?)
Publication date: 27 May 2008
Published in: (Search for Journal in Brave)
Abstract: Let be a closed manifold of Sasaki type. A polarization of is defined by a Reeb vector field, and for one such, we consider the set of all Sasakian metrics compatible with it. On this space, we study the functional given by the squared -norm of the scalar curvature. We prove that its critical points, or canonical representatives of the polarization, are Sasakian metrics that are transversally extremal. We define a Sasaki-Futaki invariant of the polarization, and show that it obstructs the existence of constant scalar curvature representatives. For a fixed CR structure of Sasaki type, we define the Sasaki cone of structures compatible with this underlying CR structure, and prove that the set of polarizations in it that admit a canonical representative is open.
Full work available at URL: https://arxiv.org/abs/math/0604325
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