305 research outputs found
The Laplacian coflow on almost-abelian Lie groups
We find explicit solutions of the Laplacian coflow of structures on
seven-dimensional almost-abelian Lie groups. Moreover, we construct new
examples of solitons for the Laplacian coflow which are not eigenforms of the
Laplacian and we exhibit a solution, which is not a soliton, having a bounded
interval of existence
Closed G-structures on non-solvable Lie groups
We investigate the existence of left-invariant closed G-structures on
seven-dimensional non-solvable Lie groups, providing the first examples of this
type. When the Lie algebra has trivial Levi decomposition, we show that such a
structure exists only when the semisimple part is isomorphic to
and the radical is unimodular and centerless.
Moreover, we classify unimodular Lie algebras with non-trivial Levi
decomposition admitting closed G-structures.Comment: 13 pages, to appear in Revista Matematica Complutens
Remarks on homogeneous solitons of the G-Laplacian flow
We show the existence of expanding solitons of the G-Laplacian flow on
non-solvable Lie groups, and we give the first example of a steady soliton that
is not an extremally Ricci pinched G-structure.Comment: 6 page
- …