We study left-invariant generalized K\"ahler structures on almost abelian Lie groups, i.e., solvable groups with a codimension-one normal subgroup. In particular, we classify six-dimensional which admit complex structure and establish of those have Hermitian whose fundamental 2-form is $\partial \bar \partial$-closed. obtain classification determine the 6-dimensional compact solvmanifolds admit...

Abstract We define solitons for the generalized Ricci flow on an exact Courant algebroid. then a family of flows left-invariant Dorfman brackets algebroid over simply connected nilpotent Lie group, generalizing bracket in way that might make this new useful study geometric such as flow. provide explicit examples both constructions Heisenberg group. also discuss solutions to

This article concerned on the study of signature submanifolds for curves under Lie group actions SE(2), SA(2) and for surfaces under SE(3). Signature submanifold is a regular submanifold which its coordinate components are differential invariants of an associated manifold under Lie group action, and therefore signature submanifold is a key for solving equivalence problems.

In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, r...