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Journal ArticleDOI

Duals of timelike Sabban curves in de Sitter n -space

Shyuichi Izumiya, +1 more
- 11 May 2018 - 
- Vol. 109, Iss: 2, pp 31
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TLDR
In this paper, generalized Sabban frames of non-lightlike curves on the de Sitter dual hypersurfaces of timelike Sabban curves were defined and investigated. But the singularities of the deSitter dual hypergraphs were not investigated.
Abstract: 
In this paper, we define generalized Sabban frames of non-lightlike curves on $$S_{1}^{n}$$ and investigate the singularities of de Sitter dual hypersurfaces of timelike Sabban curves.

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Citations
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Journal ArticleDOI

Curves and singularities, by J. W. Bruce and P. J. Giblin. Pp 222. 1984. ISBN 0-521-24945-7 (Hardback) £25, 27091-X (Paperback) £8·95 (Cambridge University Press)

D. R. J. Chillingworth
- 01 Mar 1986 - 
Posted ContentDOI

Singularities of Non-Developable Ruled Surface with Spacelike Ruling

Rashad Abdel-baky, +1 more
TL;DR: In this paper, the singularities of the spherical indicatrix and evolute of spacelike ruled surface with spacel-like ruling were studied, and the authors gave an example to illustrate their results.
Journal ArticleDOI

Singularities for Focal Sets of Timelike Sabban Curves in de Sitter 3-Space

Yongqiao Wang, +3 more
- 22 Nov 2022 - 
TL;DR: In this article , the authors defined evolutes and focal surfaces of timelike Sabban curves in de Sitter space and showed that the singularities of the focal surfaces correspond to the locus of the polar vectors of osculating de Sitters subspaces.
References
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Journal ArticleDOI

Curves and singularities, by J. W. Bruce and P. J. Giblin. Pp 222. 1984. ISBN 0-521-24945-7 (Hardback) £25, 27091-X (Paperback) £8·95 (Cambridge University Press)

D. R. J. Chillingworth
- 01 Mar 1986 - 
MonographDOI

Curves and singularities : a geometrical introduction to singularity theory

J. W. Bruce, +1 more
- 26 Nov 1992 - 
TL;DR: In this paper, the authors introduce a gravitational catastrophe machine and a set of generic properties of curves, such as transversality, normal values, regular values and smooth manifolds.
Book

Curves and Singularities

J. W. Bruce, +1 more
Book

The Unfolding and Determinacy Theorems for Subgroups of A and K

James Damon
TL;DR: The algebra of adequate homomorphism and determinacy theorems of unfolding and unfolding are studied in this article. But the algebra is not algebraic in the sense of algebraic determinacy.
Book

Differential Geometry from a Singularity Theory Viewpoint

Shyuichi Izumiya, +3 more
TL;DR: Differential Geometry from a Singularity Theory Viewpoint as mentioned in this paper provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces, using singularity theory to capture some key geometric features of surfaces.