Submanifolds of almost quaternionic skew-Hermitian manifolds

TL;DR

This paper studies various submanifolds within almost quaternionic skew-Hermitian manifolds, providing theoretical classifications and explicit examples in symmetric spaces to deepen understanding of their geometric structures.

Contribution

It classifies and constructs explicit examples of different submanifolds in almost quaternionic skew-Hermitian manifolds, especially in the torsion-free case.

Findings

Classification of submanifolds including almost symplectic, complex, pseudo-Hermitian, and quaternionic types.

Explicit examples of these submanifolds in semisimple quaternionic skew-Hermitian symmetric spaces.

Insights into the geometric structures of these submanifolds in the torsion-free setting.

Abstract

We investigate several classes of submanifolds of almost quaternionic skew-Hermitian manifolds $(M^{4n}, Q, \omega)$, including almost symplectic, almost complex, almost pseudo-Hermitian and almost quaternionic submanifolds. In the torsion-free case, we realize each type of submanifold considered in the theoretical part by constructing explicit examples of submanifolds of semisimple quaternionic skew-Hermitian symmetric spaces.