SUBSPACES OF A PARA-QUATERNIONIC HERMITIAN VECTOR SPACE

Vector valued hermitian and quaternionic modular forms

almost-quaternionic Hermitian manifolds

In this note we prove that if the fundamental 4-form of an almost-quaternionic Hermitian manifold (M,Q, g) of dimension 4n ≥ 8 satisfies the conformal-Killing equation, then (M,Q, g) is quaternionic-Kähler.

Cohomological Invariants of Quaternionic Skew-hermitian Forms

We define a complete system of invariants en,Q, n ≥ 0 for quaternionic skew-hermitian forms, which are twisted versions of the invariants en for quadratic forms. We also show that quaternionic skew-hermitian forms defined over a field of 2-cohomological dimension at most 3 are classified by rank, discriminant, Clifford invariant and Rost invariant.

Hermitian and quaternionic Hermitian structures on tangent bundles

We review the theory of quaternionic Kähler and hyperkähler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and with its well estabilished canonical complex structure. With an extra almost Hermitian structure on M it is possible to find a quaternionic Hermitian structure on TM , which is quaternionic Kähler if, and only if, D ...

Almost Hermitian Structures and Quaternionic Geometries

Gray & Hervella gave a classification of almost Hermitian structures (g, I) into 16 classes. We systematically study the interaction between these classes when one has an almost hyper-Hermitian structure (g, I, J,K). In general dimension we find at most 167 different almost hyper-Hermitian structures. In particular, we obtain a number of relations that give hyperKäher or locally conformal hyper...