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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 823809, 20 pages
Research Article

Singularities of Focal Surfaces of Null Cartan Curves in Minkowski 3-Space

1School of Mathematics Science, Harbin Normal University, Harbin 150500, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
3School of Mathematics, Changchun Normal University, Changchun 130032, China

Received 28 June 2012; Accepted 28 August 2012

Academic Editor: Gabriel Turinici

Copyright © 2012 Zhigang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Singularities of the focal surfaces and the binormal indicatrix associated with a null Cartan curve will be investigated in Minkowski 3-space. The relationships will be revealed between singularities of the above two subjects and differential geometric invariants of null Cartan curves; these invariants are deeply related to the order of contact of null Cartan curves with tangential planar bundle of lightcone. Finally, we give an example to illustrate our findings.