The Lie algebra generated by gradient vector fields

2026/07/29 by Bettina Kazandjian, Omar Mohsen, Eugenio Pozzoli
Mathematics · #math.DG #math.OC #msc:17B66 #msc:47F10 #msc:58D05

paper · pdf

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

Let M be a smooth compact manifold, and g a smooth non-degenerate symmetric bilinear form on TM. We prove that every smooth vector field can be written as a finite linear combination of iterated Lie brackets of gradient vector fields.

Citations

• Small-time approximate controllability of bilinear Schrödinger equations and diffeomorphisms

Related

• The Lie algebra preserving a degenerate bilinear form
• Vector fields invariant under a linear action of a compact Lie group
• Double bracket structures on Poisson manifolds
• Generalized double bracket vector fields
• Lie Algebras of vector fields on convenient manifolds