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

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Journal of New Theory, no.42, pp.94-107, 2023 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.53570/jnt.1213002
  • Journal Name: Journal of New Theory
  • Journal Indexes: TR DİZİN (ULAKBİM)
  • Page Numbers: pp.94-107
  • Çanakkale Onsekiz Mart University Affiliated: Yes


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.