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Octonionic Calabi-Yau theorem

Semyon AleskerPeter Gordon
Dec 2022
摘要
On a certain class of 16-dimensional manifolds a new class of Riemannianmetrics, called octonionic K\"ahler, is introduced and studied. It is anoctonionic analogue of K\"ahler metrics on complex manifolds and of HKT-metricsof hypercomplex manifolds. Then for this class of metrics an octonionic versionof the Monge-Amp\`ere equation is introduced and solved under appropriateassumptions. The latter result is an octonionic version of the Calabi-Yautheorem from K\"ahler geometry.
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