Hopf differentials and curvature line flows on time-like CMC surfaces

2025/10/28 by Ando, Naoya, Umehara, Masaaki
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.24221

Abstract

We investigate the relationship between the Hopf differentials and the curvature line flows on time-like constant mean curvature (CMC) surfaces in Lorentzian 3-space forms. In particular, when the Hopf differential is non-degenerate, the index of a curvature line flow at an umbilic point depends precisely on the remainder of its order modulo four.

Citations

• Umbilics of surfaces in the Lorentz-Minkowski 3-space

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