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An
application of the Duistermaat–Heckman theorem and its
extensions in Sasaki geometry
Charles P Boyer, Hongnian Huang and Eveline Legendre |
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Geometry & Topology 22 (2018) 4205–4234
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Abstract |
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Building on an idea laid out by Martelli, Sparks and Yau (2008), 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 thereof we get that the Einstein–Hilbert functional attains its minimal value and each Sasaki cone possesses at least one Reeb vector field with vanishing transverse Futaki invariant. |
Keywords
Futaki invariant, constant scalar curvature metrics,
Duistermaat–Heckman theorem, equivariant localisation,
Sasaki and Kahler geometry
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Mathematical Subject Classification 2010
Primary: 53B99, 53CXX, 53DXX
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References |
Publication
Received: 28 August 2017
Accepted: 28 June 2018
Published: 6 December 2018
Proposed: Simon Donaldson
Seconded: Tobias H Colding, Jean-Pierre Otal
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Authors |
| Charles P Boyer | |
| Department of Mathematics and
Statistics University of New Mexico Albuquerque, NM United States |
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| Hongnian Huang | |
| Department of Mathematics and
Statistics University of New Mexico Albuquerque, NM United States |
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| Eveline Legendre | |
| Institut de Mathematiques de
Toulouse Université Paul Sabatier Toulouse France |
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