Lc helices and harmonic curvatures in space forms (hypersurface)

TL;DR

This paper introduces LC helices in space forms, characterizing their properties using harmonic curvatures and extending results to 3-dimensional spaceforms.

Contribution

It defines LC helices in space forms and provides new characterizations based on harmonic curvatures, extending prior work on Euclidean space.

Findings

Characterization of LC helices via harmonic curvatures

Extension of results to 3-dimensional spaceforms

New insights into curve geometry in space forms

Abstract

In n-dimensional Euclidean space E^n, harmonic curvatures of a non-degenerate curve defined by \"Ozdamar and Hacisaliho\u{g}lu [4]. In this paper, We define a new type of curves called LC helix when the angle between tangent of this curve and LC parallel vector field in space form is constant. Furthermore, several characterizations of these curves by using its harmonic curvatures are obtained. Particularly, in the 3-dimensional spaceform we obtain the results [5].