A $G_2$-Hilbert functional in $G_2$-geometry

Panagiotis Gianniotis; George Zacharopoulos

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arXiv · 2505.06872

A $G_2$-Hilbert functional in $G_2$-geometry

Panagiotis Gianniotis·George Zacharopoulos

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Abstract

In this paper we introduce a new functional on the space of $G_2$-structures which we call the $G_2$-Hilbert functional. It is uniquely determined by a few basic principles inspired by the Einstein-Hilbert functional in Riemannian Geometry, and it has similar variational behaviour with it. For instance, torsion-free and nearly $G_2$-structures are saddle critical points of the volume-normalized $G_2$-Hilbert functional. This allows us to uniquely distinguish two new flows of $G_2$-structures, which can be considered as analogues of the Ricci flow in $G_2$-geometry.

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BibTeX RIS

Panagiotis Gianniotis, George Zacharopoulos. 2025-05-11. A $G_2$-Hilbert functional in $G_2$-geometry. https://arxiv.org/abs/2505.06872

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