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Journal Articles São Paulo Journal of Mathematical Sciences Year : 2021

Geometric structures and configurations of flags in orbits of real forms

Abstract

This is an introduction and a survey on geometric structures modelled on closed orbits of real forms acting on spaces of flags. We focus on 3-manifolds and the flag space of all pairs of a point and a line containing it in $\mathbf P(\mathbf C^3)$. It includes a description of general flag structures which are not necessarily flat and a combinatorial description of flat structures through con- figurations of flags in closed orbits of real forms. We also review volume and Chern-Simons invariants for those structures.
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Dates and versions

hal-03377097 , version 1 (15-10-2021)

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Elisha Falbel, Antonin Guilloux, Qingxue Wang. Geometric structures and configurations of flags in orbits of real forms. São Paulo Journal of Mathematical Sciences, 2021, 15 (1), pp.175-213. ⟨10.1007/s40863-020-00175-3⟩. ⟨hal-03377097⟩
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