On Strong r-Helix Submanifolds and Special Curves

TL;DR

This paper explores the properties of special curves on strong r-helix submanifolds in Euclidean space, establishing relationships with lines of curvature, geodesics, and slant helices.

Contribution

It introduces new relations between strong r-helix submanifolds and various special curves, enhancing understanding of their geometric interactions.

Findings

Relations between strong r-helix submanifolds and lines of curvature

Connections between geodesics and r-helix structures

Characterization of slant helices on these submanifolds

Abstract

In this paper, we investigate special curves on a strong r-helix submanifold in Euclidean n-space E n. Also, we give the important relations between strong r-helix submanifolds and the special curves such as line of curvature, geodesic and slant helix.