Nice pseudo-Riemannian nilsolitons

16 Jul 2021  ·  Diego Conti, Federico A. Rossi ·

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. read more

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Differential Geometry 53C25 (Primary) 53C50, 53C30, 22E25 (Secondary)