Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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