Related papers: Laplacian solitons on nilpotent Lie groups

Motivated by analogous results in locally conformal symplectic geometry, we study different classes of G$_2$-structures defined by a locally conformal closed 3-form. In particular, we give a complete characterization of invariant exact…

We study the Laplacian coflow and the modified Laplacian coflow of $G_2$-structures on the $7$-dimensional Heisenberg group. For the Laplacian coflow we show that the solution is always ancient, that is it is defined in some interval…

We study the condition in which G2-structures are introduced by a non closed four-form, although they are satisfying locally conformal conditions.All solutions are found in the case when the Lee form of G2-structures is non-zero and…

Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras.…

Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…

We consider left-invariant $G_2$-structures on $7$-dimensional almost Abelian Lie groups. Also, we characterise the associated torsion forms and the full torsion tensor according to the Lie bracket $A$ of the corresponding Lie algebra. In…

For G a Lie group acting on a symplectic manifold $(M,\omega)$ preserving a pair of Lagrangians $L_0$, $L_1$, under certain hypotheses not including equivariant transversality we construct a G-equivariant Floer cohomology of $L_0$ and…

We find a one-parameter family of non-isomorphic nilpotent Lie algebras $\mathfrak{g}_a$, with $a \in [0,\infty)$, of real dimension eight with (strongly non-nilpotent) complex structures. By restricting $a$ to take rational values, we…

A manifold is said to be $n$-plectic if it is equipped with a closed, nondegenerate $(n+1)$-form. This thesis develops the theory of \emph{relative $n$-plectic structures}, where the classical condition is replaced by a closed,…

We determine the equivariant real structures on nilpotent orbits and the normalizations of their closures for the adjoint action of a complex semisimple algebraic group on its Lie algebra.

We study post-Lie algebra structures on pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$, motivated by nil-affine actions of Lie groups. We prove existence results for such structures depending on the interplay of the algebraic…

We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3).…

In this paper we give the list of all 7-dimensional nilpotent real Lie algebras that admit a contact structure. Based on this list, we describe all 7-dimensional nilmanifolds that admit an invariant contact structure.

Cocalibrated G_2-structures are structures naturally induced on hypersurfaces in Spin(7)-manifolds. Conversely, one may start with a seven-dimensional manifold M endowed with a cocalibrated G_2-structure and construct via the Hitchin flow a…

We investigate left-invariant ${\rm G}_2^*$-structures on 7-dimensional Lie groups, focusing on those whose holonomy algebras are indecomposable and of type III, the latter meaning that the socle of the holonomy representation is maximal.…

Nearly $G_2$-structures define positive Einstein metrics in $7$ dimensions and are critical points, up to scale, for a geometric flow of co-closed $G_2$-structures with good analytic properties called the modified $G_2$-Laplacian co-flow.…

We explicitly describe the solution of the G$_2$-Laplacian flow starting from an extremally Ricci-pinched closed G$_2$-structure on a compact 7-manifold and we investigate its properties. In particular, we show that the solution exists for…

We continue the algebraic study of almost inner derivations of Lie algebras over a field of characteristic zero and determine these derivations for free nilpotent Lie algebras, for almost abelian Lie algebras, for Lie algebras whose…

The algebraic properties of drift-flux two-phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two fluids we consider equation of states of polytropic gases. We perform a classification…

We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on $\R^8$ which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex…