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

Authors : Saniye Can, Çetin Camci

Pages : 94-107

Doi:10.53570/jnt.1213002

View : 14 | Download : 7

Publication Date : 2023-03-31

Article Type : Research

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