arXiv subjects

M. W. Mansouri

Publications and source records attributed to M. W. Mansouri.

9 recordsLinked to original sources

arXiv2026

Three-Dimensional Real Affine Lie Groups

We classify all left-invariant real affine connections in dimension three. Our approach reduces the three-dimensional problem to a two-dimensional one by decomposing each left-invariant affine connection into a two-dimensional part and an additional one-dimensional component. After characterizing all possible two-dimensional left-invariant affine connections, we return to the three-dimensional setting to obtain a simplified description of all three-dimensional left-invariant affine connections. We then explicitly solve the resulting simplified quadratic equations and perform a refined analysis up to isomorphism, leading to a complete classification. Furthermore, we determine several geometric and algebraic properties of these structures, including the Novikov, associative, radiant, and bi-symmetric conditions, as well as geodesic completeness.

math.SG↗

arXiv2026

Balanced Hermitian structures on twisted cartesian products

We study Hermitian structures on twisted cartesian products $(\mathfrak{g}_{(ρ_{1},ρ_{2})},\mathrm{J},\cal{K})$ of two Hermitian Lie algebras according to two representations $ρ_{1}$ and $ρ_{2}$. We give the conditions on $(\mathfrak{g}_{(ρ_{1},ρ_{2})},\mathrm{J},\cal{K})$ to be balanced and locally conformally balanced. As an application we classify six-dimensional balanced Hermitian twisted cartesian products Lie algebras.

math.AG↗

arXiv2026

Eight-Dimensional Symplectic Nilpotent Lie Groups with Lagrangian Normal Subgroups: A Complete Classification

We investigate symplectic nilpotent Lie groups with Lagrangian normal subgroups. We show that there exists a bijection between the isomorphism classes of nilpotent Lie groups with Lagrangian normal subgroups and the isomorphism classes of geodesically complete, flat, nilpotent Lie groups with Lagrangian extension cohomology class. Finally, we provide a complete classification of eight-dimensional symplectic nilpotent Lie groups with Lagrangian normal subgroups, identifying exactly ninety-five such groups. As a consequence, we obtain a complete classification of eight-dimensional symplectic filiform real Lie groups.

math.SG↗

arXiv2025

Eight-dimensional non completely reducible symplectic Lie algebras

A non completely reducible symplectic Lie algebra is a symplectic Lie algebra which cannot be symplectically reduced to the trivial symplectic Lie algebra. Our aim is to provide a complete classification, up to symplectomorphism of non completely reducible symplectic Lie algebras in dimensions $n \leq 8$ and, furthermore, to provide a complete description of symplectic Lie algebras admitting one-dimensional isotropic ideals.

math.SG↗

arXiv2024

On solvable complete symplectic Lie algebras

In this paper, we are interested in solvable complete Lie algebras, over the field $\K=\R$ or $\mathbb{C}$, which admit a symplectic structure. Specifically, important classes are studied, and a description of complete Lie Algebra with the dimension of nilradical less or equal than six, which supported symplectic structure is given.

math.DG↗

arXiv2024

Cosymplectic Jacobi-Jordan Algebras

We introduce the notion of cosymplectic structure on Jacobi-Jordan algebras, and we state that they are related to symplectic Jacobi-Jordan algebras. We show, in particular, that they support a right-skew-symmetric product. We also study the double extension constructions of cosymplectic Jacobi-Jordan algebras and give a complete classification in dimension five.

math.RA↗

arXiv2024

A complete classification of symplectic forms on six-dimensional Frobeniusian real Lie algebras

In this paper, we give a complete classification of symplectic structures on six-dimensional Frobeniusian solvable Lie algebras, up to symplectomorphism. We provide a scheme to classify the isomorphism classes of six-dimensional Frobeniusian solvable Lie algebras whose exact form has a Lagrangian ideal. We complete our classification by considering Frobeniusian solvable Lie algebras without Lagrangian ideal.

math.SG↗

arXiv2023

Eight-dimensional symplectic non-solvable Lie algebras

In this paper, we classify eight-dimensional non-solvable Lie algebras that support a symplectic structure. As well as a complete classification is given, up to symplectomorphism, of eight-dimensional symplectic non-solvable Lie algebras.

math.SG↗

arXiv2022

On cosymplectic Lie Algebras

We give some properties of cosymplectic Lie algebras, we show, in particular, that they support a left symmetric product. We also give some constructions of cosymplectic Lie algebras, as well as a classification in three and five-dimensional cosymplectic Lie algebras.

math.SG↗