Integrability theorems and conformally constant Chern scalar curvature metrics in almost Hermitian geometry

Mehdi Lejmi, Markus Upmeier

Research output: Contribution to journalArticlepeer-review

Abstract

The various scalar curvatures on an almost Hermitian manifold are studied, in particular with respect to conformal variations. We show several integrability theorems, which state that two of these can only agree in the Kähler case. Our main question is the existence of almost Kähler metrics with conformally constant Chern scalar curvature. This problem is completely solved for ruled manifolds and in a complementary case where methods from the Chern-Yamabe problem are adapted to the non-integrable case. Also a moment map interpretation of the problem is given, leading to a Futaki invariant and the usual picture from geometric invariant theory.
Original languageEnglish
Pages (from-to)1603 – 1645
Number of pages43
JournalCommunications in Analysis and Geometry
Volume28
Issue number7
DOIs
Publication statusPublished - 7 Dec 2020

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