On the diagonalization of the Ricci flow on Lie groups

Details On the diagonalization of the Ricci flow on Lie groups On the diagonalization of the Ricci flow on Lie groups

2011-10-18

arxiv.org/abs/1110.4003v1

Mathematics

Differential Geometry

11 pages

Scientific paper

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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