Zindler-type hypersurfaces in R^4

Yves Martinez-Maure (1) , David Rochera (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 Basque Center for Applied Mathematics

In this paper the definition of Zindler-type hypersurfaces is introduced in R^c4 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.

Mots clés: Zindler curve; Hypersurface of constant width; Curve of constant width; Hedgehog 2000 MSC: 52A20; 53D05; 53A07; Zindler hypersurface

Domaines: Mathématiques [math]

Yves Martinez-Maure, David Rochera. Zindler-type hypersurfaces in R^4. 2022. ⟨hal-03725365v1⟩