Harmonic torsion of algebraic generalized Ricci solitons and the structure of solvable extensions

Abstract

We prove harmonicity for nonshrinking algebraic generalized Ricci solitons and for all algebraic generalized Ricci solitons on solvable Lie algebras. In the solvable setting, we characterize expanding solitons by normal extensions of generalized nilsolitons, and derive a sharp rank bound.