Constant negative Gaussian curvature tori and their singularities

Tatsumasa Ura

doi:10.21099/tkbjm/1541559651

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July 2018 Constant negative Gaussian curvature tori and their singularities

Tatsumasa Ura

Abstract

We construct constant negative Gaussian curvature tori with one family of planar curvature lines in Euclidean 3-space. We show that these tori are wave fronts. The singularities of these tori are studied.

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Tatsumasa Ura. "Constant negative Gaussian curvature tori and their singularities." Tsukuba J. Math. 42 (1) 65 - 95, July 2018. https://doi.org/10.21099/tkbjm/1541559651

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Received: 23 February 2018; Revised: 12 July 2018; Published: July 2018

First available in Project Euclid: 7 November 2018

MathSciNet: MR3873532

zbMATH: 07055225

Digital Object Identifier: 10.21099/tkbjm/1541559651

Subjects:

Primary: 53A05

Secondary: 35L70 , 57R45

Keywords: constant negative Gaussian curvature torus , sine-Gordon equation , singularity

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