Abstract

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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 323-339
Launched on MUSE
2020-01-23
Open Access
No
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