Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves

Year 2023, Issue: 42, 94 - 107, 31.03.2023

Saniye Can , Çetin Camcı

https://doi.org/10.53570/jnt.1213002

Abstract

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.

Keywords

Generalised cross product, S-manifolds, Legendre curves

Supporting Institution

This study is supported by the Office of Scientific Resarch Projects Coordination at Çanakkale Onsekiz Mart University

Project Number

FDK-2021-3520

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