On the diagonalization of the Ricci flow on Lie groups

Jorge Lauret; Cynthia Will

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arXiv · 1110.4003

On the diagonalization of the Ricci flow on Lie groups

Jorge Lauret·Cynthia Will

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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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Jorge Lauret, Cynthia Will. 2011-10-18. On the diagonalization of the Ricci flow on Lie groups. https://arxiv.org/abs/1110.4003

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