Some aspects of normal curve on smooth surface under isometry

• Autorzy: Singh Kuljeet , Sharma Sandeep , Bhardwaj Arun Kumar

Identyfikatory

DOI

10.1515/dema-2024-0017

• Języki publikacji: EN

Abstrakty

EN

The normal curve is a space curve that plays an important role in the field of differential geometry. This research focuses on analyzing the properties of normal curves on smooth immersed surfaces, considering their invariance under isometric transformations. The primary contribution of this article is to explore the requirements for the image of a normal curve that preserves its invariance under isometric transformations. In this article, we investigate the invariant condition for the component of the position vector of the normal curves under isometry and compute the expression for the normal and geodesic curvature of such curves. Moreover, it has been investigated that the geodesic curvature and Christoffel symbols remain unchanged under the isometry of surfaces in R3.

Słowa kluczowe

EN

normal curves; isometry; geodesic; normal curvature; orthonormal frame

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240017
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Singh Kuljeet

• School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, Jammu and Kashmir, India

autor

Sharma Sandeep

• School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, Jammu and Kashmir, India

autor

Bhardwaj Arun Kumar

• Department of Mathematics and Astronomy, University of Lucknow, Lucknow-226025, Uttar Pradesh, India

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).