Discrete asymptotic nets with constant affine mean curvature
In this paper we define the class of constant affine mean curvature (CAMC) discrete asymptotic nets, which contains the well-known classes of affine spheres and affine minimal asymptotic nets. This class is defined by considering fields of compatible interpolating quadrics, i.e., quadrics that have...
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| Veröffentlicht in: | Beiträge zur Algebra und Geometrie 2024-09, Vol.65 (3), p.601-621 |
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| container_title | Beiträge zur Algebra und Geometrie |
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| creator | de Vargas, Anderson Reis Craizer, Marcos |
| description | In this paper we define the class of constant affine mean curvature (CAMC) discrete asymptotic nets, which contains the well-known classes of affine spheres and affine minimal asymptotic nets. This class is defined by considering fields of compatible interpolating quadrics, i.e., quadrics that have common tangent planes at the edges of the net. We show that, for CAMC asymptotic nets, ruled discrete asymptotic nets is equivalent to ruled compatible interpolating quadrics. Moreover, we prove discrete counterparts of some known properties of the Demoulin transform of a smooth CAMC surface. |
| doi_str_mv | 10.1007/s13366-023-00707-w |
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| subjects | Algebra Algebraic Geometry Asymptotic properties Convex and Discrete Geometry Curvature Geometry Mathematics Mathematics and Statistics Original Paper |
| title | Discrete asymptotic nets with constant affine mean curvature |
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