Zindler-type hypersurfaces in R^4

In this paper the definition of Zindler-type hypersurfaces is introduced in $\mathbb{R}^4$ as a generalization of planar Zindler curves. After recalling some properties of planar Zindler curves, it is shown that Zindler hypersurfaces satisfy similar properties. Techniques from quaternions and symple...

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Detalles Bibliográficos
Autores: Martinez-Maure, Y., Rochera, D.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2022
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1519
Acceso en línea:http://hdl.handle.net/20.500.11824/1519
https://doi.org/10.1016/j.geomphys.2022.104664
Access Level:acceso embargado
Palabra clave:Zindler hypersurface
Zindler curve
Hypersurface of constant width
Constant width curves
Hedgehogs
Descripción
Sumario:In this paper the definition of Zindler-type hypersurfaces is introduced in $\mathbb{R}^4$ as a generalization of planar Zindler curves. After recalling some properties of planar Zindler curves, it is shown that Zindler hypersurfaces satisfy similar properties. Techniques from quaternions and symplectic geometry are used. Moreover, each Zindler hypersurface is fibrated by space Zindler curves that correspond, in the convex case, to some space curves of constant width lying on the associated hypersurface of constant width and with the same symplectic area.