Open Access
Research Article
Characterizations of osculating curve under isometry using Darboux frame in Euclidean 3-space
Kuljeet Singhkulljeet83@gmail.comSchool of Mathematics Shri Mata Vaishno Devi UniversityKatra, Jammu and Kashmir, 182320, IndiaView full profile → , *Sandeep SharmaCorresponding authorsandeep.greater123@gmail.comSchool of Mathematics Shri Mata Vaishno Devi UniversityKatra, Jammu and Kashmir, 182320, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Oct 2024
- Published Online:
- 01 May 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDSGT-2024-10012
- Pages:
- 15–29
Abstract
In this paper, we present a systematic study on the characterization of osculating curves under isometries using the Darboux frame in place of the Frenet frame. We further investigate the conditions for the invariance of such curves on regular surfaces embedded in Euclidean 3-space under isometric transformations. The present analysis specifically focuses on the application of the Darboux frame {𝒯, 𝒫, 𝒰}. Furthermore, we investigate how the position vector of an osculating curve on regular surfaces is affected by isometric transformations, analyzing its behavior under different orientations, specifically along the unit tangent vector 𝒯, the unit normal 𝒰, and 𝒫 = 𝒰 × 𝒯.
Keywords
Subject Classifications
51M0553A1553A0553A04
References
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