Semi-integrable almost hyperhermitian structures

Abstract

In this work, we introduce a family of almost hyperhermitian structures that we call semi-integrable. We subdivide them into four disjoint classes and show that each class is non-empty. Finally, we construct semi-integrable almost hyperhermitian structures on all reductive Lie algebras of compact type and dimension $4n$, with $n\ge 2$.

22 pages