A remark on the quaternionic Monge-Ampere equation on foliated manifolds.

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). [ABSTRACT FROM AUTHOR]