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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 1157–1174 | Cite as

On Moduli Spaces of Ricci Solitons

  • Fabio PodestàEmail author
  • Andrea Spiro
Article

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 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 \(S_{f}\times\mathcal{C}^{\infty}(M)\), 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.

Keywords

Ricci soliton Ebin slice Space of Riemannian metrics 

Mathematics Subject Classification

53C25 53C21 

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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Dip. di Matematica “U. Dini”Università di FirenzeFirenzeItaly
  2. 2.Scuola di Scienze e TecnologieUniversità di CamerinoCamerino (Macerata)Italy

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