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arXiv · 2410.21103

Stability of nearly K\"ahler and nearly parallel $G_2$-manifolds

Enric Solé-Farré
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Abstract

We investigate generalisations of Hitchin's functionals, whose critical points correspond to nearly K\"ahler and nearly parallel $G_2$-structures. Our focus is on the gradient flow of these functionals and the spectral decomposition of their Hessians with respect to natural indefinite inner products. We introduce a Morse-like index for these functionals, termed the Hitchin index. We prove this index provides a lower bound for the Einstein co-index and explore its relationship with the deformation theory of $G_2$- and $\operatorname{Spin}(7)$-conifolds.

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Enric Solé-Farré. 2024-10-28. Stability of nearly K\"ahler and nearly parallel $G_2$-manifolds. https://arxiv.org/abs/2410.21103

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