arXiv subjects
Publications and source records attributed to S. Ruhallah Ahmadi.
If $X$ is a connected complex manifold with $d_X = 2$ that admits the holomorphic and transitive action of a (connected) Lie group $G$, then the action extends to an action of the complexification $\hat{G}$ of $G$ on $X$ except when either the unit disk or else a strictly pseudoconcave homogeneous complex manifold is involved as base or fiber in some homogeneous fibration of $X$.
Suppose $G$ is a connected complex Lie group and $Γ$ is a discrete subgroup such that $X := G/Γ$ is Kähler and the codimension of the top non--vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less than or equal to two. We show that $G$ is solvable and a finite covering of $X$ is biholomorphic to a product $C\times A$, where $C$ is a Cousin group and $A$ is $\{e \}$, $\mathbb C$, $\mathbb C^*$, or $\mathbb C^*\times\mathbb C^*$.
Let $f:V\times V\to F$ be a totally arbitrary bilinear form defined on a finite dimensional vector space $V$ over a a field $F$, and let $L(f)$ be the subalgebra of $\gl(V)$ of all skew-adjoint endomorphisms relative to $f$. Provided $F$ is algebraically closed of characteristic not 2, we determine all $f$, up to equivalence, such that $L(f)$ is reductive. As a consequence, we find, over an arbitrary field, necessary and sufficient conditions for $L(f)$ to be simple, semisimple or isomorphic to $\sl(n)$ for some $n$.