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arXiv · 2107.07767

Nice pseudo-Riemannian nilsolitons

Diego Conti·Federico A. Rossi
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Abstract

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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Diego Conti, Federico A. Rossi. 2021-07-16. Nice pseudo-Riemannian nilsolitons. https://doi.org/10.1016/j.geomphys.2021.104433

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