Bertrand and hyperelastic curves on Riemannian manifolds

Authors

  • Abdussamet Çalışkan Fatsa Vocational School, Accounting and Tax Applications Ordu University, Ordu, Turkey

DOI:

https://doi.org/10.3842/umzh.v78i5-6.8357

Keywords:

Bertrand curve, hyperelastic curve, Riemannian manifold, umbilical,, totally geodesic submanifold

Abstract

UDC 514.76, 514.75

We introduce the notion of Bertrand curves on Riemannian manifolds. The necessary conditions for a curve on a Riemannian manifold to be a Bertrand curve are obtained in the form of differential equations. Then, necessary and sufficient conditions are found for the Bertrand curve to remain a Bertrand curve in the ambient space. Moreover, we examine the influence of Bertrand and hyperelastic curves on the geometric properties of isometric immersions. We study the relationship between these types of curves and umbilical submanifolds. Finally, we present the criteria for the Bertrand curve to be a hyperelastic curve in the ambient space along an immersion.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 5-6, 2026.

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Published

29.05.2026

Issue

Vol. 78 No. 5-6 (2026)

Section

Research articles