Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves
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.
Supporting Institution
This study is supported by the Office of Scientific Resarch Projects Coordination at Çanakkale Onsekiz Mart University
Project Number
FDK-2021-3520
References
- K. Yano, On Structures Defined by a Tensor Field f of Type (1,1) Satisfying f^3+f=0, Tensor 14 (1963) 99–109.
- S. I. Goldberg, K. Yano, On Normal Globally Framed f-manifolds, Tohoku Mathematical Journal 22 (1970) 362–370.
- D. E. Blair, Geometry of Manifolds with Structural Group U(n)×O(s), Journal of Differential Geometry 4 (1970) 155–167.
- A. Sarkar, S. K. Hui, M. Sen, A Study on Legendre Curves in 3-Dimensional Trans-Sasakian Manifolds, Lobachevski Journal of Mathematics 35 (2014) 11–18.
- C. Özgür, Ş. Güvenç, On Biharmonic Legendre Curves in S-space Forms, Turkish Journal of Mathematics 38 (2014) 454–461.
- Ç. Camcı, Extended Cross Product in a 3-dimensional Almost Contact Metric Manifold with Applications to Curve Theory, Turkish Journal of Mathematics 36 (2012) 305–318.
- M. Z. Williams, F. M. Stein, A Triple Product of Vectors in Four-space, Mathematics Magazine 4 (1964) 230–235.
- S. Ishihara, Normal Structure f Satisfying f^3+f=0, Mathematical Seminar Reports 18 (1966) 36–47
- J. S. Kim, M. K. Dwivedi, M. M. Tripathi, Ricci Curvature of Integral Submanifolds of an S-space Form, Bulletin of the Korean Mathematical Society 44 (2007) 395–406.
- I. Hasegawa, Y. Okuyama, T. Abe, On p-th Sasakian Manifolds, Journal of Hokkaido University of Education (Section II A) 37 (1) (1986) 1–16.
- O. Aléssio, Differential Geometry of Intersection Curves in R^4 of Three Implicit Surfaces, Computer Aided Geometry Design 26 (2009) 455–471.
Abstract
Project Number
FDK-2021-3520
References
- K. Yano, On Structures Defined by a Tensor Field f of Type (1,1) Satisfying f^3+f=0, Tensor 14 (1963) 99–109.
- S. I. Goldberg, K. Yano, On Normal Globally Framed f-manifolds, Tohoku Mathematical Journal 22 (1970) 362–370.
- D. E. Blair, Geometry of Manifolds with Structural Group U(n)×O(s), Journal of Differential Geometry 4 (1970) 155–167.
- A. Sarkar, S. K. Hui, M. Sen, A Study on Legendre Curves in 3-Dimensional Trans-Sasakian Manifolds, Lobachevski Journal of Mathematics 35 (2014) 11–18.
- C. Özgür, Ş. Güvenç, On Biharmonic Legendre Curves in S-space Forms, Turkish Journal of Mathematics 38 (2014) 454–461.
- Ç. Camcı, Extended Cross Product in a 3-dimensional Almost Contact Metric Manifold with Applications to Curve Theory, Turkish Journal of Mathematics 36 (2012) 305–318.
- M. Z. Williams, F. M. Stein, A Triple Product of Vectors in Four-space, Mathematics Magazine 4 (1964) 230–235.
- S. Ishihara, Normal Structure f Satisfying f^3+f=0, Mathematical Seminar Reports 18 (1966) 36–47
- J. S. Kim, M. K. Dwivedi, M. M. Tripathi, Ricci Curvature of Integral Submanifolds of an S-space Form, Bulletin of the Korean Mathematical Society 44 (2007) 395–406.
- I. Hasegawa, Y. Okuyama, T. Abe, On p-th Sasakian Manifolds, Journal of Hokkaido University of Education (Section II A) 37 (1) (1986) 1–16.
- O. Aléssio, Differential Geometry of Intersection Curves in R^4 of Three Implicit Surfaces, Computer Aided Geometry Design 26 (2009) 455–471.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Project Number | FDK-2021-3520 |
| Publication Date | March 31, 2023 |
| Submission Date | December 1, 2022 |
| Published in Issue | Year 2023 Issue: 42 |
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