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April 24, 2026International Electronic Journal of Geometry

Characterizations of f-Osculating Curves in 3 and 4 Dimensional Euclidean Spaces

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Authors

ASAbsos Ali ShaikhPBPushpinder BadyalSSSandeep Sharma

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Overview

Characterizes f-osculating curves in three and four dimensional spaces, suggesting important geometric properties.

Key Points

  • This research aims to define and analyze the properties of f-osculating curves in three and four dimensional Euclidean spaces.
  • Introduced the concept of f-osculating curves in Euclidean spaces.
  • Established necessary and sufficient conditions for these curves.
  • Examined cases with constant curvature functions and their effects on remaining curvature.
  • Defined the requirements for unit-speed curves to be f-osculating curves in 3D and 4D.
  • Derived relationships among various curvature functions for these curves.
  • Analyzed the behavior when certain curvature functions are constant.

Cite This Study

Shaikh et al. (2026) studied this question.

synapsesocial.com/papers/69eb0a94553a5433e34b4992https://doi.org/10.36890/iejg.1762742
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Osculating surfaces with modified orthogonal frame in Euclidean 3-space2026
  2. 2Geometrical Analysis of Osculating Curves in Minkowski Space 𝔼142026
  3. 3On admissible $f$-rectifying curves in 3D pseudo-Galilean geometry2026
  4. 4Behavior of spatial curves under different transformations in Euclidean 4-space2025
  5. 5On Equiform Rectifying, Normal and Osculating Curves in Minkowski Space-Time2024