Year: 2026
Type: preprint
Abstract: We give an explicit description of the orbits of the split real form $G_{2(2)}$ on the complex flag manifolds of $G_2$ and study their induced invariant CR structures. In particular we study their Levi forms and show that all possible cases in the simple homogeneous setting occur, namely Levi nondegeneracy, $k$-nondegeneracy for $2\leq k\leq 3$, and holomorphic degeneracy. Moreover, following the classical approach to orbits on flag manifolds, we give equations for these homogeneous CR manifolds.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Università degli Studi di Parma
OpenAlex ID: W7221055035