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arXiv · 1708.03006

An application of the Duistertmaat--Heckman Theorem and its extensions in Sasaki Geometry

Charles P. Boyer·Hongnian Huang·Eveline Legendre
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Abstract

Building on an idea laid out by Martelli--Sparks--Yau, we use the Duistermaat-Heckman localization formula and an extension of it to give rational and explicit expressions of the volume, the total transversal scalar curvature and the Einstein--Hilbert functional, seen as functionals on the Sasaki cone (Reeb cone). Studying the leading terms we prove they are all proper. Among consequences we get that the Einstein-Hilbert functional attains its minimal value and each Sasaki cone possess at least one Reeb vector field with vanishing transverse Futaki invariant.

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Charles P. Boyer, Hongnian Huang, Eveline Legendre. 2017-08-09. An application of the Duistertmaat--Heckman Theorem and its extensions in Sasaki Geometry. https://doi.org/10.2140/gt.2018.22.4205

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