Subspaces of a para-quaternionic Hermitian vector space

Details Subspaces of a para-quaternionic Hermitian vector space Subspaces of a para-quaternionic Hermitian vector space

2010-11-12

arxiv.org/abs/1011.2947v1

Mathematics

Differential Geometry

Scientific paper

Let $(\tilde Q,g) $ be a para-quaternionic Hermitian structure on the real vector space $V$. By referring to the tensorial presentation $(V, \tilde{Q},g) \simeq (H^2 \otimes E^{2n}, \mathfrak{sl}(H),\omega^H \otimes \omega^E)$, we give an explicit description, from an affine and metric point of view, of main classes of subspaces of $V$ which are invariantly defined with respect to the structure group of $\tilde{Q}$ and $(\tilde{Q},g)$ respectively.

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