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arXiv · 2108.01937

A note on invariant description of $SU(2)$-structures in dimension 5

Kamil Niedzialomski
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Abstract

We develop an invariant approach to $SU(2)$--structures on spin $5$--manifolds. We characterize (via spinor approach) the subspaces in the spinor bundle which induce the same group isomorphic to $SU(2)$. Moreover, we show how to induce quaternionic structure on the contact distribution of considered $SU(2)$--structure. We conclude with the invariance of certain components of the covariant derivative $\nabla\varphi$, where $\varphi$ is any spinor field defining considered $SU(2)$--structure. This shows, what expected, that (at least some of) the intrinsic torsion modules, can be derived invariantly with the spinorial approach.

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Kamil Niedzialomski. 2021-08-04. A note on invariant description of $SU(2)$-structures in dimension 5. https://arxiv.org/abs/2108.01937

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