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arXiv · 1302.4307

On moduli spaces of Ricci solitons

Fabio Podesta'·Andrea Spiro
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Abstract

We study deformations of shrinking Ricci solitons on a compact manifold M, generalising the classical theory of deformations of Einstein metrics. Using appropriate notions of twisted slices S_f inside the space of all Riemannian metrics on M, we define the infinitesimal solitonic deformations and the local solitonic pre-moduli spaces. We prove the existence of a finite dimensional submanifold of S_f x C^infty(M), which contains the pre-moduli space of solitons around a fixed shrinking Ricci soliton as an analytic subset. We define solitonic rigidity and give criteria which imply it.

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Fabio Podesta', Andrea Spiro. 2013-02-18. On moduli spaces of Ricci solitons. https://arxiv.org/abs/1302.4307

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