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 MongeAmp`ere equation has always a unique solution for every basic datum. This approach includes the study of the equation on SU(3).
A remark on the quaternionic Monge-Ampère equation on foliated manifolds
Giovanni Gentili;Luigi Vezzoni
2023-01-01
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 MongeAmp`ere equation has always a unique solution for every basic datum. This approach includes the study of the equation on SU(3).
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