JOURNAL ARTICLE

Conformal trajectories in three-dimensional space forms.

  • Published In: International Journal of Geometric Methods in Modern Physics, 2025, v. 22, n. 1. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: López, Rafael; Munteanu, Marian Ioan 3 of 3

Abstract

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds M 3 . Given a conformal vector field V ∈ (M 3) , a conformal trajectory of V is a regular curve γ in M 3 satisfying ∇ γ ′ γ ′ = q V × γ ′ , for some fixed nonzero constant q ∈ ℝ. In this paper, we study the conformal trajectories in the space forms ℝ 3 , 3 and ℍ 3 . For (non-Killing) conformal vector fields in 3 (respectively, in ℍ 3 ), we prove that conformal trajectories have constant curvature and its torsion is a linear combination of trigonometric (respectively, hyperbolic) functions on the arc-length parameter. In the case of Euclidean space ℝ 3 , we obtain the same result for the radial vector field and characterizing all conformal trajectories. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Geometric Methods in Modern Physics. 2025/01, Vol. 22, Issue 1, p1
  • Document Type:Article
  • Subject Area:Astronomy and Astrophysics
  • Publication Date:2025
  • ISSN:0219-8878
  • DOI:10.1142/S021988782450258X
  • Accession Number:181093186
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