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arXiv · 1712.06398

An energy functional on the universal spinor bundle

Leonardo Bagaglini
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Abstract

We study an energy functional on the universal spinor bundle over a closed $n$-dimensional spin manifold $M$. The critical points of this functional, which is modelled on the total torsion functional of $G_2$-structures in seven dimensions, are pairs of Ricci-flat metrics and real parallel spinor fields provided that $n$ equals $3$ or $7$. We then modify the functional to obtain the analogue in arbitrary dimensions. Finally we apply the universal spinor bundle approach to solve some ODEs problems concerning $G_2$-structures.

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Leonardo Bagaglini. 2017-12-18. An energy functional on the universal spinor bundle. https://arxiv.org/abs/1712.06398

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