Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves
This study generalizes the cross product defined in 3-dimensional almost contact metric manifolds and describes a new generalized cross product for n=1 in (2n+s)-dimensional framed metric manifolds. Moreover, it studies some of the proposed product’s basic properties. It also performs characterizati...
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| Format: | Article |
| Language: | English |
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Naim Çağman
2023-03-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/2806387 |
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| _version_ | 1849723710934614016 |
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| author | Çetin Camcı Saniye Can |
| author_facet | Çetin Camcı Saniye Can |
| author_sort | Çetin Camcı |
| collection | DOAJ |
| description | This study generalizes the cross product defined in 3-dimensional almost contact metric manifolds and describes a new generalized cross product for n=1 in (2n+s)-dimensional framed metric manifolds. Moreover, it studies some of the proposed product’s basic properties. It also performs characterizations of the curvature of a Legendre curve on an S-manifold and calculates the curvature of a Legendre curve. Furthermore, it shows that Legendre curves are also biharmonic curves. Next, this study observes that a Legendre curve of osculating order 5 on S-manifolds is imbedded in the 3-dimensional K-contact space. Lastly, the current paper discusses the need for further research. |
| format | Article |
| id | doaj-art-4a9dbf2b9a914b4c90be70ebd97c9901 |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-4a9dbf2b9a914b4c90be70ebd97c99012025-08-20T03:10:57ZengNaim ÇağmanJournal of New Theory2149-14022023-03-01429410710.53570/jnt.12130022425Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre CurvesÇetin Camcı0https://orcid.org/0000-0002-0122-559XSaniye Can1https://orcid.org/0000-0003-4991-325XÇanakkale Onsekiz Mart University, Faculty of Science, Department of MathematicsÇanakkale Onsekiz Mart University, Faculty of Science, Department of MathematicsThis study generalizes the cross product defined in 3-dimensional almost contact metric manifolds and describes a new generalized cross product for n=1 in (2n+s)-dimensional framed metric manifolds. Moreover, it studies some of the proposed product’s basic properties. It also performs characterizations of the curvature of a Legendre curve on an S-manifold and calculates the curvature of a Legendre curve. Furthermore, it shows that Legendre curves are also biharmonic curves. Next, this study observes that a Legendre curve of osculating order 5 on S-manifolds is imbedded in the 3-dimensional K-contact space. Lastly, the current paper discusses the need for further research.https://dergipark.org.tr/en/download/article-file/2806387generalised cross products-manifoldslegendre curves |
| spellingShingle | Çetin Camcı Saniye Can Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves Journal of New Theory generalised cross product s-manifolds legendre curves |
| title | Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves |
| title_full | Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves |
| title_fullStr | Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves |
| title_full_unstemmed | Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves |
| title_short | Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves |
| title_sort | generalized cross product in 2 s dimensional framed metric manifolds with application to legendre curves |
| topic | generalised cross product s-manifolds legendre curves |
| url | https://dergipark.org.tr/en/download/article-file/2806387 |
| work_keys_str_mv | AT cetincamcı generalizedcrossproductin2sdimensionalframedmetricmanifoldswithapplicationtolegendrecurves AT saniyecan generalizedcrossproductin2sdimensionalframedmetricmanifoldswithapplicationtolegendrecurves |