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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Main Authors: Çetin Camcı, Saniye Can
Format: Article
Language:English
Published: Naim Çağman 2023-03-01
Series:Journal of New Theory
Subjects:
Online Access:https://dergipark.org.tr/en/download/article-file/2806387
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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