$G_2$-manifolds and the ADM formalism

Ryohei Chihara

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arXiv · 1806.00454

$G_2$-manifolds and the ADM formalism

Ryohei Chihara

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Abstract

In this paper we study a Hamiltonian function on the cotangent bundle of the space of Riemannian metrics on a 3-manifold $M$ and prove the orbits of the constrained Hamiltonian dynamical system correspond to $G_2$-manifolds foliated by hypersurfaces diffeomorphic to $M\times \mathrm{SO}(3)$.

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Ryohei Chihara. 2018-06-01. $G_2$-manifolds and the ADM formalism. https://arxiv.org/abs/1806.00454

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