Quaternions, Monge–Ampère Structures and k-Surfaces

Graham Smith
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Graham Smith: Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Departamento de Matemática

Chapter Chapter 5 in Surveys in Geometry II, 2024, pp 145-177 from Springer

Abstract: Abstract In Labourie (Geom Funct Anal 7: 496–534, 1997) Labourie developed 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 Smith (Math Ann 335(1): 57–95, 2013).

Keywords: Extrinsic curvature; Monge–Ampère equation; J-holomorphic curves; 53A05; 12E15; 35J96 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-3-031-43510-2_5

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