Singularities of Indefinite Hypersurfaces and Indefinite Surfaces along Timelike Curves in Nullcone with Index Two
In this paper, a class of indefinite hypersurfaces and a class of indefinite surfaces generated by timelike curves located in nullcone in 4-dimensional semi-Euclidean space with index 2 are discussed. Using the unfolding theory in singularity theory, the singularities of the indefinite hypersurfaces...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/5859410 |
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| _version_ | 1849305508140285952 |
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| author | Xue Song Zhigang Wang |
| author_facet | Xue Song Zhigang Wang |
| author_sort | Xue Song |
| collection | DOAJ |
| description | In this paper, a class of indefinite hypersurfaces and a class of indefinite surfaces generated by timelike curves located in nullcone in 4-dimensional semi-Euclidean space with index 2 are discussed. Using the unfolding theory in singularity theory, the singularities of the indefinite hypersurfaces and the indefinite surfaces are classified and the different kinds of singularities are estimated by means of a geometric invariant σ. Meanwhile, the definition of osculating nullcone is presented; the study shows that the differential geometric invariant σ of timelike curves measured also the order of the contact between a timelike curve and a osculating nullcone ONCv0⁎. Finally, some relevant counterexamples are indicated. |
| format | Article |
| id | doaj-art-014ec91f1cce42da8bf4e6d69ec8834d |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-014ec91f1cce42da8bf4e6d69ec8834d2025-08-20T03:55:24ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/58594105859410Singularities of Indefinite Hypersurfaces and Indefinite Surfaces along Timelike Curves in Nullcone with Index TwoXue Song0Zhigang Wang1School of Mathematical Sciences, Harbin Normal University, Harbin 150025, ChinaSchool of Mathematical Sciences, Harbin Normal University, Harbin 150025, ChinaIn this paper, a class of indefinite hypersurfaces and a class of indefinite surfaces generated by timelike curves located in nullcone in 4-dimensional semi-Euclidean space with index 2 are discussed. Using the unfolding theory in singularity theory, the singularities of the indefinite hypersurfaces and the indefinite surfaces are classified and the different kinds of singularities are estimated by means of a geometric invariant σ. Meanwhile, the definition of osculating nullcone is presented; the study shows that the differential geometric invariant σ of timelike curves measured also the order of the contact between a timelike curve and a osculating nullcone ONCv0⁎. Finally, some relevant counterexamples are indicated.http://dx.doi.org/10.1155/2018/5859410 |
| spellingShingle | Xue Song Zhigang Wang Singularities of Indefinite Hypersurfaces and Indefinite Surfaces along Timelike Curves in Nullcone with Index Two Journal of Function Spaces |
| title | Singularities of Indefinite Hypersurfaces and Indefinite Surfaces along Timelike Curves in Nullcone with Index Two |
| title_full | Singularities of Indefinite Hypersurfaces and Indefinite Surfaces along Timelike Curves in Nullcone with Index Two |
| title_fullStr | Singularities of Indefinite Hypersurfaces and Indefinite Surfaces along Timelike Curves in Nullcone with Index Two |
| title_full_unstemmed | Singularities of Indefinite Hypersurfaces and Indefinite Surfaces along Timelike Curves in Nullcone with Index Two |
| title_short | Singularities of Indefinite Hypersurfaces and Indefinite Surfaces along Timelike Curves in Nullcone with Index Two |
| title_sort | singularities of indefinite hypersurfaces and indefinite surfaces along timelike curves in nullcone with index two |
| url | http://dx.doi.org/10.1155/2018/5859410 |
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