2024/04/12 by Jun-ichi Inoguchı, Inoguchi, Junichi, Shimpei Kobayashi +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2404.08235
We classify weakly complete constant Gaussian curvature -1-1 and K ≠ 0 via the harmonicity of the Lagrangian and Legendrian Gauss maps. We then show that a spectral parameter deformation of the Lagrangian harmonic Gauss map gives a harmonic map into the hyperbolic two-space for -1< K<0 or the two-sphere for K>0, respectively. Consequently, weakly complete constant Gaussian curvature surfaces with -1 < K <0 are in one-to-one correspondence with holomorphic quadratic differentials on the unit disk or the complex plane.