Triharmonic Legendre curves on Lorentzian Heisenberg Space

This paper investigates triharmonic Legendre curves in the context of Lorentzian Heisenberg space (H3,g), a framework that merges concepts from differential geometry and theoretical physics. Triharmonic curves, defined by their stationarity with respect to the first variation of the energy functional, offer rich geometric properties. We derive the fundamental equations governing these curves and explore their behavior under the unique curvature of Lorentzian Heisenberg space (H3,g). The study reveals how the interplay between the curve’s triharmonic nature and the space’s Lorentzian structure leads to distinctive geometric features, including relativity and geometric modeling. The findings enhance the understanding of how triharmonic curves behave in complex geometrical settings, contributing to the broader discourse on the significance of curvature in higher-dimensional spaces. This research opens avenues for further exploration of triharmonic properties in other geometric framework.