تقرير
Invariant surfaces with coordinate finite-type Gauss map in simply isotropic space
| العنوان: | Invariant surfaces with coordinate finite-type Gauss map in simply isotropic space |
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| المؤلفون: | Kelleci, Alev, da Silva, Luiz C. B. |
| المصدر: | J. Math. Anal. Appl. 495 (2021) 124673 |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53A35, 53B25, 53C42 |
| الوصف: | We consider the extrinsic geometry of surfaces in simply isotropic space, a three-dimensional space equipped with a rank 2 metric of index zero. Since the metric is degenerate, a surface normal cannot be unequivocally defined based on metric properties only. To understand the contrast between distinct choices of an isotropic Gauss map, here we study surfaces with a Gauss map whose coordinates are eigenfunctions of the surface Laplace-Beltrami operator. We take into account two choices, the so-called minimal and parabolic normals, and show that when applied to simply isotropic invariant surfaces the condition that the coordinates of the corresponding Gauss map are eigenfunctions leads to planes, certain cylinders, or surfaces with constant isotropic mean curvature. Finally, we also investigate (non-necessarily invariant) surfaces with harmonic Gauss map and show this characterizes constant mean curvature surfaces. Comment: 24 pages (23 in the published version), 3 figures; Keywords: Simply isotropic space, Gauss map, helicoidal surface, parabolic revolution surface, invariant surface, Cayley-Klein geometry |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.jmaa.2020.124673 |
| URL الوصول: | http://arxiv.org/abs/2004.12221 |
| رقم الأكسشن: | edsarx.2004.12221 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.jmaa.2020.124673 |
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