Year: 2020
Type: preprint
Abstract: We study holomorphic GL(2) and SL(2) geometries on compact complex manifolds. We show that a compact Kähler manifold of complex even dimension higher than two admitting a holomorphic GL(2)-geometry is covered by a compact complex torus. We classify compact Kähler-Einstein manifolds and Fano manifolds bearing holomorphic GL(2)-geometries. Among the compact Kähler-Einstein manifolds we prove that the only examples bearing holomorphic GL(2)-geometry are those covered by compact complex tori, the three dimensional quadric and those covered by the three dimensional Lie ball (the non compact dual of the quadric).
Source: arXiv (Cornell University)
Authors: Biswas, Indranil, Dumitrescu, Sorin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3014323787