Codimension one Ricci soliton subgroups of nilpotent Iwasawa groups
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- by Víctor Sanmartín-López;
- Trans. Amer. Math. Soc.
- DOI: https://doi.org/10.1090/tran/9394
- Published electronically: May 8, 2025
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Abstract:
Any expanding homogeneous Ricci soliton (in particular any homogeneous Einstein manifold of negative scalar curvature) can be obtained, up to isometry, as a solvable extension of a Lie subgroup of a nilpotent Iwasawa group $N$ whose induced metric is a Ricci soliton. By nilpotent Iwasawa group we mean the nilpotent Lie group $N$ of the Iwasawa decomposition associated with a symmetric space of non-compact type. Motivated by this fact, in this paper we classify codimension one Lie subgroups of any nilpotent Iwasawa group $N$ whose induced metric is a Ricci soliton.References
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Bibliographic Information
- Víctor Sanmartín-López
- Affiliation: CITMAga, 15782 Santiago de Compostela, Spain; and Department of Mathematics, Universidade de Santiago de Compostela, Spain
- ORCID: 0000-0001-7052-9258
- Email: victor.sanmartin@usc.es
- Received by editor(s): September 18, 2023
- Received by editor(s) in revised form: April 8, 2024, and November 22, 2024
- Published electronically: May 8, 2025
- Additional Notes: The author was supported by Grant PID2022-138988NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF, EU, and by ED431C 2023/31 (Xunta de Galicia).
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
- MSC (2020): Primary 53C40, 53C35, 53C42
- DOI: https://doi.org/10.1090/tran/9394