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- Title
Rigidity of SU<sub>n</sub>-Type Symmetric Spaces.
- Authors
Batat, Wafaâ; Hall, Stuart James; Murphy, Thomas; Waldron, James
- Abstract
We prove that the bi-invariant Einstein metric on |$SU_{2n+1}$| is isolated in the moduli space of Einstein metrics, even though it admits infinitesimal deformations. This gives a non-Kähler, non-product example of this phenomenon adding to the famous example of |$\mathbb{C}\mathbb{P}^{2n}\times \mathbb{C}\mathbb{P}^{1}$| found by Koiso. We apply our methods to derive similar solitonic rigidity results for the Kähler–Einstein metrics on "odd" Grassmannians. We also make explicit a connection between non-integrable deformations and the dynamical instability of metrics under Ricci flow.
- Subjects
EINSTEIN, Albert, 1879-1955; SYMMETRIC spaces; RICCI flow; GRASSMANN manifolds; EINSTEIN manifolds; INFINITESIMAL geometry
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 3, p2066
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad077