Spatial Generalized Octonionic Curves

This study investigates curves in a 7-dimensional space, represented by spatial generalized octonion-valued functions of a single variable, where the general octonions include real, split, semi, split semi, quasi, split quasi, and para octonions. We begin by constructing a new frame, referred to as...

Full description

Bibliographic Details
Published in:	Axioms
Main Authors:	Mücahit Akbıyık, Jeta Alo, Seda Yamaç Akbıyık
Format:	Article
Language:	English
Published:	MDPI AG 2025-08-01
Subjects:	generalized octonions curvatures Frenet–Serret frame formulae
Online Access:	https://www.mdpi.com/2075-1680/14/9/665

Similar Items

4-dimensional pseudo-Galilean geometry
by: Salim Yüce, et al.
Published: (2021-12-01)

Geometry of Curves with Fractional Derivatives in Lorentz Plane
by: Meltem Öğrenmiş
Published: (2022-03-01)

The Geometry of Bezier Curves in Minkowski 3−Space
by: Ayşe Yılmaz Ceylan
Published: (2023-03-01)

One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode
by: Areej A. Almoneef, et al.
Published: (2023-08-01)

Smarandache Curves Of Null Quaternionic Curves In Minkowski 3-space
by: T. Kahraman
Published: (2018-05-01)

Some Characteristic Properties of Non-Null Curves in Minkowski 3-Space <inline-formula><math display="inline"><semantics><mrow><msubsup><mo>𝔼</mo><mn>1</mn><mi>3</mi></msubsup></mrow></semantics></math></inline-formula>
by: Areej A. Almoneef, et al.
Published: (2023-06-01)

On Generalized Tribonacci Octonions
by: Arzu Özkoç Öztürk
Published: (2019-10-01)

Generating Bézier curves for medical image reconstruction
by: H.S. Abdel-Aziz, et al.
Published: (2021-04-01)

Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space
by: Nadia Alluhaibi, et al.
Published: (2023-10-01)

Equiform rectifying curves in Galilean space G4
by: M. Elzawy, et al.
Published: (2023-11-01)

Surface Family Pair with Bertrand Pair as Mutual Curvature Lines in Three-Dimensional Lie Group
by: Awatif Al-Jedani, et al.
Published: (2023-08-01)

Surface Family Pair with Bertrand Pair as Common Geodesic Curves in Galilean 3-Space 𝔾<sub>3</sub>
by: Areej A. Almoneef, et al.
Published: (2023-05-01)

A Study on $f$-Rectifying Curves in Euclidean $n$-Space
by: Zafar Iqbal, et al.
Published: (2021-09-01)

Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame
by: Vahide Bulut
Published: (2018-12-01)

On the Octonion Cross Wigner Distribution of 3-D Signals
by: Łukasz Błaszczyk, et al.
Published: (2022-05-01)

Disturbance Interval Observer-Based Robust Constrained Control for Unmanned Aerial Vehicle Path Following
by: Yaping Song, et al.
Published: (2023-01-01)

The Generalization of Gaussians and Leonardo’s Octonions
by: Vieira Renata Passos Machado, et al.
Published: (2023-03-01)

COMBINED ALGORITHMS FOR CONSTRUCTING A SOLUTION TO THE TIME–OPTIMAL PROBLEM IN THREE-DIMENSIONAL SPACE BASED ON THE SELECTION OF EXTREME POINTS OF THE SCATTERING SURFACE
by: Pavel D. Lebedev, et al.
Published: (2022-12-01)

A Surface Family with a Mutual Geodesic Curve in Galilean 3-Space <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">G</mi><mn>3</mn></msub></semantics></math></inline-formula>
by: Awatif Al-Jedani, et al.
Published: (2023-07-01)

Horadam Octonions
by: Karataş Adnan, et al.
Published: (2017-12-01)

Special helices on equiform differential geometry of timelike curves in E_1^4
by: Fatma Bulut
Published: (2021-12-01)

Fundamental Results of Cyclic Codes over Octonion Integers and Their Decoding Algorithm
by: Muhammad Sajjad, et al.
Published: (2022-12-01)

Applications of Differential Geometry of Curves in Roads Design
by: Burlacu Adrian, et al.
Published: (2023-12-01)

A Parallel Algorithm for Dividing Octonions
by: Aleksandr Cariow, et al.
Published: (2021-10-01)

Octonion-valued $ b $-metric spaces and results on its application
by: Xiu-Liang Qiu, et al.
Published: (2025-05-01)

Discrete Octonion Linear Canonical Transform: Definition and Properties
by: Wen-Biao Gao
Published: (2024-03-01)

Spacelike developable surfaces through a common line of curvature in Minkowski 3-space
by: Cai-Yun LI, et al.
Published: (2015-09-01)

Shape Sensing of Cantilever Column Using Hybrid Frenet–Serret Homogeneous Transformation Matrix Method
by: Peng Zhang, et al.
Published: (2024-04-01)

Some remarks regarding the $(p,q)-$Fibonacci and Lucas octonion polynomials
by: Arzu Özkoç Öztürk, et al.
Published: (2018-03-01)

Developable Ruled Surfaces Generated by the Curvature Axis of a Curve
by: Ferhat Taş, et al.
Published: (2023-11-01)

Computational Characterization of the Multiplication Operation of Octonions via Algebraic Approaches
by: Ray-Ming Chen
Published: (2024-04-01)

The Third Order Jacobsthal Octonions: Some Combinatorial Properties
by: Cerda-Morales Gamaliel
Published: (2018-12-01)

Octonion-based transform moments for innovative stereo image classification with deep learning
by: Mohamed Amine Tahiri, et al.
Published: (2024-02-01)

Non-Orthogonal Serret–Frenet Parametrization Applied to Path Following of B-Spline Curves by a Mobile Manipulator
by: Filip Dyba, et al.
Published: (2024-09-01)

Behavior of spatial curves under different transformations in Euclidean 4-space
by: Badyal Pushpinder, et al.
Published: (2025-07-01)

Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$
by: Mehmet Bektaş, et al.
Published: (2022-09-01)

Construction and Analysis of Smarandache Curves for Integral Binormal Curves in Euclidean 3-Space
by: Hasnaa Baizeed, et al.
Published: (2025-09-01)

Translation-Based Embeddings with Octonion for Knowledge Graph Completion
by: Mei Yu, et al.
Published: (2022-04-01)

The non-orthogonal Serret–Frenet parametrization applied to the path following problem of a manipulator with partially known dynamics
by: Alicja Mazur, et al.
Published: (2023-06-01)

On Third-Order Bronze Fibonacci Numbers
by: Mücahit Akbiyik, et al.
Published: (2021-10-01)