Pseudo-Riemannian Almost Hypercomplex Homogeneous Spaces with Irreducible Isotropy

Key Points

• The research aims to classify certain homogeneous pseudo-Riemannian manifolds with a specific structure and isotropy.
• Classification of homogeneous pseudo-Riemannian manifolds of index 4.
• Analysis of invariant almost hyper-Hermitian structures.
• Evaluation of H-irreducible isotropy groups.
• All classified manifolds are hyper-Kahler and flat except in dimension 12.
• Established the unique characteristics of these homogeneous spaces.