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

Naoya Ando; Masaaki Umehara

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arXiv · 2510.24221

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

Naoya Ando·Masaaki Umehara

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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.

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Naoya Ando, Masaaki Umehara. 2025-10-28. Hopf differentials and curvature line flows on time-like CMC surfaces. https://arxiv.org/abs/2510.24221

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