On the diagonalization of the Ricci flow on Lie groups

Lauret, Jorge; Will, Cynthia

doi:10.1090/S0002-9939-2013-11813-7

On the diagonalization of the Ricci flow on Lie groups
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by Jorge Lauret and Cynthia Will PDF

Proc. Amer. Math. Soc. 141 (2013), 3651-3663 Request permission

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 one of them, and only the bracket of disjoint pairs can be a nonzero multiple 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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