Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space
In this paper we analyzed the problem of studying locally the scalar curvature S of the two dimensional kinematic surfaces obtained by the homothetic motion of a helix in Lorentz-Minkowski space E17 $\text{E}^7_1$ . We express the scalar curvature S of the corresponding kinematic surfaces as the quo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-09-01
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| Series: | Nonlinear Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nleng-2016-0012 |
| _version_ | 1818691514994262016 |
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| author | Solouma E. M. Wageeda M. M. |
| author_facet | Solouma E. M. Wageeda M. M. |
| author_sort | Solouma E. M. |
| collection | DOAJ |
| description | In this paper we analyzed the problem of studying locally the scalar curvature S of the two dimensional kinematic surfaces obtained by the homothetic motion of a helix in Lorentz-Minkowski space
E17 $\text{E}^7_1$ . We express the scalar curvature S of the corresponding kinematic surfaces as the quotient of hyperbolic functions {cosh mϕ, sinh mϕ}, and we derive the necessary and sufficient conditions for the coefficients to vanishes identically. Finally, an example is given to show two dimensional kinematic surfaces with zero scalar curvature. |
| first_indexed | 2024-12-17T12:43:07Z |
| format | Article |
| id | doaj.art-7ac5550b4efc44b6872ea414c59cc0c6 |
| institution | Directory Open Access Journal |
| issn | 2192-8010 2192-8029 |
| language | English |
| last_indexed | 2024-12-17T12:43:07Z |
| publishDate | 2017-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj.art-7ac5550b4efc44b6872ea414c59cc0c62022-12-21T21:47:52ZengDe GruyterNonlinear Engineering2192-80102192-80292017-09-016320120610.1515/nleng-2016-0012Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-spaceSolouma E. M.0Wageeda M. M.1Department of Mathematics, Faculty of Science, Beni-Suef University, Beni Suef, EgyptMathematics Department, Faculty of Science, Aswan University, Aswan, EgyptIn this paper we analyzed the problem of studying locally the scalar curvature S of the two dimensional kinematic surfaces obtained by the homothetic motion of a helix in Lorentz-Minkowski space E17 $\text{E}^7_1$ . We express the scalar curvature S of the corresponding kinematic surfaces as the quotient of hyperbolic functions {cosh mϕ, sinh mϕ}, and we derive the necessary and sufficient conditions for the coefficients to vanishes identically. Finally, an example is given to show two dimensional kinematic surfaces with zero scalar curvature.https://doi.org/10.1515/nleng-2016-0012minkowski spacekinematic surfaceshomothetic motionscalar curvature53a0553a1753b30 |
| spellingShingle | Solouma E. M. Wageeda M. M. Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space Nonlinear Engineering minkowski space kinematic surfaces homothetic motion scalar curvature 53a05 53a17 53b30 |
| title | Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space |
| title_full | Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space |
| title_fullStr | Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space |
| title_full_unstemmed | Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space |
| title_short | Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space |
| title_sort | two dimensional kinematic surfaces with constant scalar curvature in lorentz minkowski 7 space |
| topic | minkowski space kinematic surfaces homothetic motion scalar curvature 53a05 53a17 53b30 |
| url | https://doi.org/10.1515/nleng-2016-0012 |
| work_keys_str_mv | AT soloumaem twodimensionalkinematicsurfaceswithconstantscalarcurvatureinlorentzminkowski7space AT wageedamm twodimensionalkinematicsurfaceswithconstantscalarcurvatureinlorentzminkowski7space |