CURVATURE OF THE COMPLETION OF THE SPACE OF SASAKI POTENTIALS

Thomas Franzinetti

doi:10.5565/PUBLMAT6712309

Abstract

Given a compact Sasaki manifold, we endow the space of the Sasaki potentials with an analogue of the Mabuchi metric. We show that its metric completion is negatively curved in the sense of Alexandrov.

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Thomas Franzinetti. "CURVATURE OF THE COMPLETION OF THE SPACE OF SASAKI POTENTIALS." Publ. Mat. 67 (1) 447 - 468, 2023. https://doi.org/10.5565/PUBLMAT6712309

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Received: 29 January 2021; Accepted: 1 October 2021; Published: 2023

First available in Project Euclid: 19 December 2022

MathSciNet: MR4522938

zbMATH: 1509.31019

Digital Object Identifier: 10.5565/PUBLMAT6712309

Subjects:

Primary: 31C12 , 32U15 , 32W20 , 53C25 , 53C55

Keywords: energy classes , Monge–Ampère equations , negatively curved metric spaces , Sasaki manifolds

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