We study deformations of shrinking Ricci solitons on a compact manifold M, generalizing the classical theory of deformations of Einstein metrics. Using appropriate notions of twisted slices S 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, 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. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAM
On Moduli Spaces of Ricci Solitons
SPIRO, Andrea
2015-01-01
Abstract
We study deformations of shrinking Ricci solitons on a compact manifold M, generalizing the classical theory of deformations of Einstein metrics. Using appropriate notions of twisted slices S 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, 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. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAMFile | Dimensione | Formato | |
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art%3A10.1007%2Fs12220-013-9461-2.pdf
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arXiv 1302.4307v1 18 Feb 2013.pdf
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