On the diagonalization of the Ricci flow on Lie groups

WILL, CYNTHIA

Marburg

Congreso; Geometric structures on manifolds and their applications; 2012

Univ. de Marburg

The known results on the Ricci flow of low-dimensional homogeneous manifolds rely on the existence of a basis such that any diagonal invariant metric has a diagonal Ricci tensor, which considerably reduces the qualitative study of the solutions. We prove that for nilpotent Lie algebras, such bases 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. Also, some non-nilpotent examples are considered and some applications to Ricci solitons are given.