Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Conti - F. A. Rossi

Nice pseudo-Riemannian nilsolitons

created by rossi on 19 Jul 2021
modified on 27 Apr 2022


Published Paper

Inserted: 19 jul 2021
Last Updated: 27 apr 2022

Journal: J. Geom. Phys.
Volume: 173
Pages: 104433
Year: 2022

ArXiv: 2107.07767 PDF


We study nice nilpotent Lie algebras admitting a diagonal nilsoliton metric. We classify nice Riemannian nilsolitons up to dimension $9$. For general signature, we show that determining whether a nilpotent nice Lie algebra admits a nilsoliton metric reduces to a linear problem together with a system of as many polynomial equations as the corank of the root matrix. We classify nice nilsolitons of any signature: in dimension $\leq 7$; in dimension $8$ for corank $\leq 1$; in dimension $9$ for corank zero.

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