Octonionic Calabi-Yau theorem
Differential Geometry
2024-05-21 v5 Analysis of PDEs
Abstract
A new class of Riemannian metrics, called octonionic K\"ahler, is introduced and studied on a certain class of 16-dimensional manifolds. It is an octonionic analogue of K\"ahler metrics on complex manifolds and of HKT-metrics of hypercomplex manifolds. Then for this class of metrics an octonionic version of the Monge-Amp\`ere equation is introduced and solved under appropriate assumptions. The latter result is an octonionic version of the Calabi-Yau theorem from K\"ahler geometry.
Cite
@article{arxiv.2212.07857,
title = {Octonionic Calabi-Yau theorem},
author = {Semyon Alesker and Peter Gordon},
journal= {arXiv preprint arXiv:2212.07857},
year = {2024}
}
Comments
80 pages; revised version