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 for n=1 (2n+s)-dimensional framed manifolds. Moreover, it studies some of proposed product’s basic properties. It also performs characterizations curvature Legendre curve on an S-manifold calculates curve. Furthermore, shows that curves are biharmonic curves. Next, this observes osculating order 5 S-manifolds is imbedded K-contact space. Lastly, current paper discusses need further research.