Magnetic Curves in Homothetic <i>s</i>-th Sasakian Manifolds
We investigate normal magnetic curves in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mi>s</mi><mo...
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2025-01-01
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| author | Şaban Güvenç Cihan Özgür |
| author_facet | Şaban Güvenç Cihan Özgür |
| author_sort | Şaban Güvenç |
| collection | DOAJ |
| description | We investigate normal magnetic curves in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mi>s</mi><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional homothetic <i>s</i>-th Sasakian manifolds as a generalization of <i>S</i>-manifolds. We show that a curve <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> is a normal magnetic curve in a homothetic <i>s</i>-th Sasakian manifold if and only if its osculating order satisfies <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>≤</mo><mn>3</mn></mrow></semantics></math></inline-formula> and it belongs to a family of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mi>i</mi></msub></semantics></math></inline-formula>-slant helices. Additionally, we construct a homothetic <i>s</i>-th Sasakian manifold using generalized <i>D</i>-homothetic transformations and present the parametric equations of normal magnetic curves in this manifold. |
| format | Article |
| id | doaj-art-00aad1a6aad94e86bb745bec8ff1ef13 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-00aad1a6aad94e86bb745bec8ff1ef132025-01-10T13:18:27ZengMDPI AGMathematics2227-73902025-01-0113115910.3390/math13010159Magnetic Curves in Homothetic <i>s</i>-th Sasakian ManifoldsŞaban Güvenç0Cihan Özgür1Department of Mathematics, Balikesir University, 10145 Balikesir, TürkiyeDepartment of Mathematics, İzmir Democracy University, 35140 İzmir, TürkiyeWe investigate normal magnetic curves in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mi>s</mi><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional homothetic <i>s</i>-th Sasakian manifolds as a generalization of <i>S</i>-manifolds. We show that a curve <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> is a normal magnetic curve in a homothetic <i>s</i>-th Sasakian manifold if and only if its osculating order satisfies <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>≤</mo><mn>3</mn></mrow></semantics></math></inline-formula> and it belongs to a family of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mi>i</mi></msub></semantics></math></inline-formula>-slant helices. Additionally, we construct a homothetic <i>s</i>-th Sasakian manifold using generalized <i>D</i>-homothetic transformations and present the parametric equations of normal magnetic curves in this manifold.https://www.mdpi.com/2227-7390/13/1/159magnetic curve<i>θ<sub>i</sub></i>-slant curvehomothetic <i>s</i>-th Sasakian manifold |
| spellingShingle | Şaban Güvenç Cihan Özgür Magnetic Curves in Homothetic <i>s</i>-th Sasakian Manifolds Mathematics magnetic curve <i>θ<sub>i</sub></i>-slant curve homothetic <i>s</i>-th Sasakian manifold |
| title | Magnetic Curves in Homothetic <i>s</i>-th Sasakian Manifolds |
| title_full | Magnetic Curves in Homothetic <i>s</i>-th Sasakian Manifolds |
| title_fullStr | Magnetic Curves in Homothetic <i>s</i>-th Sasakian Manifolds |
| title_full_unstemmed | Magnetic Curves in Homothetic <i>s</i>-th Sasakian Manifolds |
| title_short | Magnetic Curves in Homothetic <i>s</i>-th Sasakian Manifolds |
| title_sort | magnetic curves in homothetic i s i th sasakian manifolds |
| topic | magnetic curve <i>θ<sub>i</sub></i>-slant curve homothetic <i>s</i>-th Sasakian manifold |
| url | https://www.mdpi.com/2227-7390/13/1/159 |
| work_keys_str_mv | AT sabanguvenc magneticcurvesinhomotheticisithsasakianmanifolds AT cihanozgur magneticcurvesinhomotheticisithsasakianmanifolds |