A remark on the quaternionic Monge-Ampère equation on foliated manifolds

Gentili, Giovanni; Vezzoni, Luigi

doi:10.1090/proc/16121

A remark on the quaternionic Monge-Ampère equation on foliated manifolds
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by Giovanni Gentili and Luigi Vezzoni;

Proc. Amer. Math. Soc. 151 (2023), 1263-1275

DOI: https://doi.org/10.1090/proc/16121

Published electronically: December 21, 2022

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Abstract:

Pursuing the approach of Gentili and Vezzoni [Math. Res. Not. IMRN 12 (2022), pp. 9499–9528] we study the quaternionic Monge-Ampère equation on HKT (hyperkähler with torsion) manifolds admitting an HKT foliation having corank $4$. We show that in this setting the quaternionic Monge-Ampère equation has always a unique solution for every basic datum. This approach includes the study of the equation on $\operatorname {SU}(3)$.

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