On the rigidity of the complex Grassmannians
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- by Stuart James Hall, Paul Schwahn and Uwe Semmelmann;
- Trans. Amer. Math. Soc. 378 (2025), 4335-4367
- DOI: https://doi.org/10.1090/tran/9402
- Published electronically: March 25, 2025
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Abstract:
We study the integrability to second order of the infinitesimal Einstein deformations of the symmetric metric $g$ on the complex Grassmannian of $k$-planes inside $\mathbb {C}^n$. By showing the nonvanishing of Koiso’s obstruction polynomial, we characterize the infinitesimal deformations that are integrable to second order as an explicit variety inside $\mathfrak {su}(n)$. In particular we show that $g$ is isolated in the moduli space of Einstein metrics if $n$ is odd.References
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Bibliographic Information
- Stuart James Hall
- Affiliation: School of Mathematics, Statistics, and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
- MR Author ID: 937287
- ORCID: 0000-0002-8414-1518
- Email: stuart.hall@ncl.ac.uk
- Paul Schwahn
- Affiliation: Universidade Estadual de Campinas, IMECC, Rua Sérgio Buarque de Holanda 651, 13083-859 Campinas-SP, Brazil
- MR Author ID: 1488207
- ORCID: 0000-0003-0718-3949
- Email: schwahn@ime.unicamp.br
- Uwe Semmelmann
- Affiliation: Institut für Geometrie und Topologie, Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- MR Author ID: 364613
- Email: uwe.semmelmann@mathematik.uni-stuttgart.de
- Received by editor(s): June 3, 2024
- Received by editor(s) in revised form: December 4, 2024
- Published electronically: March 25, 2025
- Additional Notes: The second author was supported by the Procope project no. 48959TL and by the BRIDGES project funded by ANR grant no. ANR-21-CE40-0017. The third author was supported by the Special Priority Program SPP 2026 “Geometry at Infinity” funded by the DFG
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 4335-4367
- MSC (2020): Primary 32Q20, 53C24, 53C25
- DOI: https://doi.org/10.1090/tran/9402