The lightcone Gauss map and the lightcone
    developable of a spacelike curve in Minkowski 3-space

Shyuichi Izumiya; Donghe Pei; Takasi Sano

doi:10.1017/S0017089500010107

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We define the notion of lightcone Gauss maps, lightcone pedal curves and lightcone developables of spacelike curves in Minkowski 3-space and establish the relationships between singularities of these objects and geometric invariants of curves under the action of the Lorentz group.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Yücesan, Ahmet Çöken, A.Ceylan and Ayyildiz, Nihat 2004. On the Darboux rotation axis of Lorentz space curve. Applied Mathematics and Computation, Vol. 155, Issue. 2, p. 345.

Izumiya, Shyuichi Kossowski, Marek Pei, Donghe and Romero Fuster, M. Carmen 2006. Singularities of lightlike hypersurfaces in Minkowski four-space. Tohoku Mathematical Journal, Vol. 58, Issue. 1,

IZUMIYA, SHYUICHI KIKUCHI, MAKOTO and TAKAHASHI, MASATOMO 2006. GLOBAL PROPERTIES OF SPACELIKE CURVES IN MINKOWSKI 3-SPACE. Journal of Knot Theory and Its Ramifications, Vol. 15, Issue. 07, p. 869.

Izumiya, Shyuichi Romero Fuster, María del Carmen and Saji, Kentaro 2009. Flat lightlike hypersurfaces in Lorentz–Minkowski 4-space. Journal of Geometry and Physics, Vol. 59, Issue. 11, p. 1528.

Chen, Liang and Izumiya, Shyuichi 2010. Singularities of Anti de Sitter torus Gauss maps. Bulletin of the Brazilian Mathematical Society, New Series, Vol. 41, Issue. 1, p. 37.

Chen, Liang Han, Qixing Pei, Donghe and Sun, Weizhi 2010. The singularities of null surfaces in Anti de Sitter 3-space. Journal of Mathematical Analysis and Applications, Vol. 366, Issue. 1, p. 256.

Pei, DongHe Kong, LingLing Sun, JianGuo and Wang, Qi 2010. Singularities of lightlike hypersurface in semi-Euclidean 4-space with index 2. Science China Mathematics, Vol. 53, Issue. 12, p. 3243.

Wang, Zhigang and Pei, Donghe 2010. Singularities of ruled null surfaces of the principal normal indicatrix to a null Cartan curve in de Sitter 3-space. Physics Letters B, Vol. 689, Issue. 2-3, p. 101.

Şahin, Tevfik and Yilmaz, Murteza 2011. The rectifying developable and the tangent indicatrix of a curve in Galilean 3-space. Acta Mathematica Hungarica, Vol. 132, Issue. 1-2, p. 154.

Wang, Zhigang Pei, Donghe Chen, Liang Kong, Lingling Han, Qixing and Turinici, Gabriel 2012. Singularities of Focal Surfaces of Null Cartan Curves in Minkowski 3‐Space. Abstract and Applied Analysis, Vol. 2012, Issue. 1,

Wang, Zhigang Pei, Donghe and Kong, Lingling 2013. Gaussian surfaces and nullcone dual surfaces of null curves in a three-dimensional nullcone with index 2. Journal of Geometry and Physics, Vol. 73, Issue. , p. 166.

Izumiya, Shyuichi and Sato, Takami 2013. Lightlike hypersurfaces along spacelike submanifolds in Minkowski space–time. Journal of Geometry and Physics, Vol. 71, Issue. , p. 30.

Liu, Haiming and Pei, Donghe 2013. Singularities of a Space Curve according to the Relatively Parallel Adapted Frame and Its Visualization. Mathematical Problems in Engineering, Vol. 2013, Issue. , p. 1.

Körpinar, Talat and Turhan, Essin 2013. Parallel surfaces to normal ruled surfaces of general helices in the sol space Sol³. Boletim da Sociedade Paranaense de Matemática, Vol. 31, Issue. 2, p. 245.

Kong, Lingling and Pei, Donghe 2014. On spacelike curves in hyperbolic space times sphere. International Journal of Geometric Methods in Modern Physics, Vol. 11, Issue. 03, p. 1450014.

Körpınar, Talat 2014. D-TANGENT SURFACES OF TIMELIKE BIHARMONIC D-HELICES ACCORDING TO DARBOUX FRAME ON NON-DEGENERATE TIMELIKE SURFACES IN THE LORENTZIAN HEISENBERG GROUP H. Boletim da Sociedade Paranaense de Matemática, Vol. 32, Issue. 1, p. 35.

Chen, Liang Izumiya, Shyuichi Pei, DongHe and Saji, Kentaro 2014. Anti de Sitter horospherical flat timelike surfaces. Science China Mathematics, Vol. 57, Issue. 9, p. 1841.

Izumiya, Shyuichi and Yıldırım, Handan 2015. Slant geometry on spacelike submanifolds of codimension two in Lorentz–Minkowski space. Journal of Geometry and Physics, Vol. 98, Issue. , p. 160.

Aydın Şekerci, Gülşah 2021. On evolutoids and pedaloids in Minkowski 3-space. Journal of Geometry and Physics, Vol. 168, Issue. , p. 104313.

Li, Pengcheng and Pei, Donghe 2021. Nullcone Fronts of Spacelike Framed Curves in Minkowski 3-Space. Mathematics, Vol. 9, Issue. 22, p. 2939.

Download full list

Article contents

The lightcone Gauss map and the lightconedevelopable of a spacelike curve in Minkowski 3-space

Abstract

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

The lightcone Gauss map and the lightconedevelopable of a spacelike curve in Minkowski 3-space

Abstract

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests