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arXiv · 2502.13748

Isometric immersions of constant curvature one metrics on the 2-sphere with two conical singularities into Euclidean 3-space: A partial solution to the Gálvez-Hauswirth-Mira problem

Zhiqiang Wei
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Abstract

In this paper, we establish a geometric correspondence between constant curvature one metrics with two conical singularities on $S^{2}$ and isometric immersions into Euclidean 3-space $\mathbb{E}^{3}$. Specifically, we explicitly construct a family of surfaces with constant curvature one, each of which is endowed with two conical singularities. This construction provides a partial solution to an open problem proposed by Gálvez, Hauswirth, and Mira (Adv in Math. 241(2013) 103-126).

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Zhiqiang Wei. 2025-03-23. Isometric immersions of constant curvature one metrics on the 2-sphere with two conical singularities into Euclidean 3-space: A partial solution to the Gálvez-Hauswirth-Mira problem. https://arxiv.org/abs/2502.13748

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