E104-04 - Forschungsbereich Angewandte Geometrie E057-16 - Fachbereich Center for Geometry and Computational Design
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Journal:
Results in Mathematics
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ISSN:
1422-6383
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Date (published):
2025
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Number of Pages:
43
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Publisher:
SPRINGER BASEL AG
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Peer reviewed:
Yes
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Keywords:
transformations; Christoffel dual; deformation
en
Abstract:
Motivated by the design of flexible nets, we classify all nets of arbitrary size
that admit a continuous family of area-preserving Combescure transformations. There are just two different classes. The nets in the first class are special cases of cone nets that have been recently studied by Kilian, Müller, and Tervooren. The second class consists of Kœnigs nets having a Christoffel dual with the same areas of corresponding faces. We apply isotropic metric duality to get a new class of flexible nets in isotropic geometry. We also study the smooth analogs of the introduced classes.
