Octonionic Calabi-Yau theorem

2022/12/15 by Semyon Alesker, Alesker, Semyon, Peter Gordon +1 · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2212.07857

openalex publication_date 2022/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new class of Riemannian metrics, called octonionic Kähler, is introduced and studied on a certain class of 16-dimensional manifolds. It is an octonionic analogue of Kähler metrics on complex manifolds and of HKT-metrics of hypercomplex manifolds. Then for this class of metrics an octonionic version of the Monge-Ampère equation is introduced and solved under appropriate assumptions. The latter result is an octonionic version of the Calabi-Yau theorem from Kähler geometry.

Cited by

• Octonionic Para-linear Self-Adjoint Operators and Spectral Decomposition

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• Singular Calabi-Yau metrics
• Geometric invariants and the Monge-Ampere equation in Kähler geometry
• The Calabi Conjecture
• A parabolic approach to the Calabi-Yau problem in HKT geometry
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