On weak r-Helix submanifolds

TL;DR

This paper explores the properties of weak r-helix submanifolds in Euclidean space, focusing on their relationship with special curves like lines of curvature, asymptotic curves, and helix lines.

Contribution

It establishes new relations between weak r-helix submanifolds and various special curves, enhancing understanding of their geometric structure.

Findings

Identified key relations between weak r-helix submanifolds and special curves.

Characterized the behavior of lines of curvature and asymptotic curves on these submanifolds.

Connected weak r-helix submanifolds with classical curve types in Euclidean space.

Abstract

In this paper, we investigate special curves on a weak r-helix submanifold in Euclidean n-space E^{n}. Also, we give the important relations between weak r-helix submanifolds and the special curves such as line of curvature, asymptotic curve and helix line.