Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry

By Semyon Alesker, Misha Verbitsky. 2005

72 citations recorded by the source corpus.

A hypercomplex manifold is a manifold equipped with a triple of complex structures I, J, K satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret these functions geometrically as potentials of HKT (hyperkähler with torsion) metrics. We prove a quaternionic analogue of A. D. Aleksandrov and ChernLevine-Nirenberg theorems.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/dc54860a66a8cd91d1e0c03c2d47c1be801cdfb4

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In Applied Mathematics

1. Misha Verbitsky
2. Semyon Alesker
3. A. Bernig
4. Franz E. Schuster
5. Joseph H. G. Fu
6. Monika Ludwig
7. Daniel Hug
8. Judit Abardia

In Geometry and Topology

1. Misha Verbitsky
2. Semyon Alesker
3. A. Bernig
4. Franz E. Schuster
5. Monika Ludwig
6. Joseph H. G. Fu
7. Judit Abardia
8. Daniel Hug

Citations in the corpus

• Quaternionic Monge-Ampère equation and Calabi problem for HKT-manifolds (2008, background): “ M. Verbitsky, February 3, 2014 the isomorphism constructed in Proposition 2.6. Let R: Λp,q I (M) −→Λ p+q,0 I (M) be the composition of the standard projection Λp,q I (M) −→P+ Λp,q I,+(M) with Re. In [AV], we defined a real structure on Λ2p,0 I (M), that is, an anticomplex involution mapping λ∈ Λ2p,0”