The Smarandache Curves on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>and Its Duality on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mr

<p>The flow of a curve is said to be inextensible if the arc length in the first case and the intrinsic curvature in the second case are preserved. In this work, we investigated the inextensible flow of a curve on $ S^2 $ according to a modified orthogonal Saban frame. Initially, we gave the definition of the modified Saban frame and then established the relations between the Frenet and the modified orthogonal Saban frames. Later, we determined the inextensible curve flow and geodesic curvature of a curve on the unit sphere using the modified orthogonal Saban frame. Also, we gave some theorems and results for special cases of the evolution of a curve on a sphere. Finally, we gave examples and their graphs for the inextensible flow equation of curvatures.</p>

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

The Smarandache Curves onS12and Its Duality onH02

Cited by 2 publications

References 4 publications

Smarandache curves in Euclidean 4- space E 4

Smarandache curves in Euclidean 4- space E 4

On the curve evolution with a new modified orthogonal Saban frame

Contact Info

Product

Resources

About