Original Article
Kyungpook Mathematical Journal 2012; 52(1): 49-59
Published online March 23, 2012
Copyright © Kyungpook Mathematical Journal.
$C$-parallel Mean Curvature Vector Fields along Slant Curves in Sasakian $3$-manifolds
Ji-Eun Lee1, Young Jin Suh2, Hyunjin Lee3
1Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, Korea
2Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea
3Graduate School of Electrical Engineering and Computer Science, Kyungpook National University, Daegu 702-701, Korea
Received: March 23, 2012; Revised: March 23, 2012; Accepted: March 23, 2012
In this article, using the example of C. Camci(cite{CAM}) we reconfirm necessary sufficient condition for a slant curve. Next, we find some necessary and sufficient conditions for a slant curve in a Sasakian $3$-manifold to have: (i) a $C$-parallel mean curvature vector field; (ii) a $C$-proper mean curvature vector field (in the normal bundle).
Keywords: Slant curves, Mean curvature vector fields, $C$-parallel, Sasakian manifolds