On the existence of homogeneous solitons of gradient type for the G$_{\mathbf 2}$-Laplacian flow
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- by Anna Fino and Alberto Raffero;
- Proc. Amer. Math. Soc. 152 (2024), 2199-2204
- DOI: https://doi.org/10.1090/proc/16755
- Published electronically: March 25, 2024
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Abstract:
In this note, we prove the existence of homogeneous gradient solitons for the G$_2$-Laplacian flow by providing the first known example of this type. This result singles out the G$_2$-Laplacian flow as the first known geometric flow admitting homogeneous gradient solitons on spaces that are one-dimensional extensions in the sense of Petersen and Wylie [Differential Geom. Appl. 84 (2022), Paper No. 101929, 29].References
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Bibliographic Information
- Anna Fino
- Affiliation: Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy; and Department of Mathematics and Statistics, Florida International University, Miami, Florida 33199
- MR Author ID: 363840
- ORCID: 0000-0003-0048-2970
- Email: annamaria.fino@unito.it, afino@fiu.edu
- Alberto Raffero
- Affiliation: Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
- MR Author ID: 1110053
- ORCID: 0000-0003-1413-0327
- Email: alberto.raffero@unito.it
- Received by editor(s): August 29, 2023
- Published electronically: March 25, 2024
- Additional Notes: The authors were supported by GNSAGA of INdAM and by the project PRIN 2022 “Real and Complex Manifolds: Geometry and Holomorphic Dynamics”. The first named author was also supported by a grant from the Simons Foundation ($\#$944448).
- Communicated by: Jiaping Wang
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2199-2204
- MSC (2020): Primary 53C10, 53C30
- DOI: https://doi.org/10.1090/proc/16755
- MathSciNet review: 4728483