2022/10/06 by Graham Smith, Smith, Graham
Mathematics · #12E15 #35J96 #53A05 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2210.02664
openalex publication_date 2022/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [15] Labourie develops a theory of immersed surfaces of prescribed extrinsic curvature which has since found widespread applications in hyperbolic geometry, general relativity, Teichmüller theory, and so on. In this chapter, we present a quaternionic reformulation of these ideas. This yields simpler proofs of the main results whilst pointing towards the higher-dimensional generalisation studied by the author in [25].