Complex Legendre duality
Differential Geometry
2024-11-21 v1 Complex Variables
Abstract
We introduce complex generalizations of the classical Legendre transform, operating on K\"ahler metrics on a compact complex manifold. These Legendre transforms give explicit local isometric symmetries for the Mabuchi metric on the space of K\"ahler metrics around any real analytic K\"ahler metric, answering a question originating in Semmes' work.
Keywords
Cite
@article{arxiv.1608.05541,
title = {Complex Legendre duality},
author = {Bo Berndtsson and Dario Cordero-Erausquin and Bo'az Klartag and Yanir A. Rubinstein},
journal= {arXiv preprint arXiv:1608.05541},
year = {2024}
}
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14 pages