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On nonsingular two-step nilpotent Lie algebras
(2014)
A 2-step nilpotent Lie algebra n is called non-singular if ad X : n → [n, n] is onto for any X /∈ [n, n]. We explore non-singular algebras in several directions, including the classification problem (isomorphism invariants), ...
On homogeneous Ricci solitons
(2014)
We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Hq,n ⊂ Λ2g∗ ⊗ g of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to ...
Curvature flows for almost-hermitian Lie groups
(2015)
We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad ...