Quasitoric manifolds homeomorphic to homogeneous spaces

Abstract

We present some classification results for quasitoric manifolds $M$ with $p_{1}(M) = -\sum a_{i}^{2}$ for some $a_{i}\in H^{2}(M)$ which admit an action of a compact connected Lie-group $G$ such that $\dim M/G \leq 1$. In contrast to Kuroki's work [7, 6] we do not require that the action of $G$ extends the torus action on $M$.