On the diagonalization of the Ricci flow on Lie groups

2011/10/18 by Jorge Lauret, Cynthia Will, Lauret, Jorge +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1110.4003

11 pages

arxiv created 2011/10/18 · arxiv updated 2011/10/19

Abstract

The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of some of them and only the bracket of disjoint pairs can be nonzero multiples of the same element. Some applications to the Ricci flow of left-invariant metrics on Lie groups concerning diagonalization are also given.

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