The twistor lifts of surfaces in 4-spaces

2025/09/26 by Ando, Naoya
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.22253

Abstract

This is a survey of the twistor lifts of surfaces in 4-spaces. In most part of this survey, the space is the Euclidean 4-space E⁴. The definitions of the Gauss maps and the twistor lifts of surfaces in E⁴ are given by complex structures of E⁴. Based on these definitions, we can understand that the Gauss maps of minimal surfaces are holomorphic and characterize isotropicity of minimal surfaces.

Citations

• Surfaces with flat normal connection in 4-dimensional space forms
• The SO(3,1)-orbits in the light cone of the 2-fold exterior power of the Minkowski 4-space
• Time-like surfaces with zero mean curvature vector in 4-dimensional neutral space forms
• Hyperbolic Twistor Spaces

Related

• The equations of Gauss, Codazzi and Ricci of surfaces in 4-dimensional space forms
• On the moduli space of isometric surfaces with the same mean curvature in 4-dimensional space forms
• Twistorial construction of minimal hypersurfaces
• Boost Invariant Surfaces with Pointwise 1-Type Gauss Map in Minkowski 4-Space E4-1
• Spacelike surfaces in De Ditter 3-space and their twistor lifts