Abstract
Zero mean curvature surfaces in the simply isotropic 3-space \({\mathbb {I}}^3\) naturally appear as intermediate geometry between geometry of minimal surfaces in \({\mathbb {E}}^3\) and that of maximal surfaces in \({\mathbb {L}}^3\). In this paper, we investigate reflection principles for zero mean curvature surfaces in \({\mathbb {I}}^3\) as with the above surfaces in \({\mathbb {E}}^3\) and \({\mathbb {L}}^3\). In particular, we show a reflection principle for isotropic line segments on such zero mean curvature surfaces in \({\mathbb {I}}^3\), along which the induced metrics become singular.
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The authors would like to express their gratitude to the referees for their comments and suggestions.
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The first author was partially supported by JSPS KAKENHI Grant Number 19K14527, and the second author by JSPS KAKENHI Grant Number 20K14306.
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The first author was partially supported by JSPS KAKENHI Grant Number 19K14527, and the second author by JSPS KAKENHI Grant Number 20K14306.
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Akamine, S., Fujino, H. Reflection Principles for Zero Mean Curvature Surfaces in the Simply Isotropic 3-space. Results Math 77, 176 (2022). https://doi.org/10.1007/s00025-022-01718-0
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DOI: https://doi.org/10.1007/s00025-022-01718-0