Bertrand Curves in $n$-Dimensional Riemann-Otsuki Space
Abstract
In this paper, we extend the classic properties of Bertrand curves in Euclidean 3-space to an $n$-dimensional Riemann-Otsuki space. We introduce the concept of infinitesimal deformations of curves within this space, and by applying the Frenet formulas concerning the contravariant component of the covariant derivative, we derive conditions under which a given deformation of a curve corresponds to a Bertrand curve in this $n$-dimensional space.
Keywords
General connections, Riemann-Otsuki space, Frenet frame, Bertrand curves
References
- T. Otsuki, Tangent Bundles of order 2 and general connections, Mathematical Journal of Okayama University 8 (2) (1958) 143--179.
- T. Otsuki, On tangent bundles of order 2 and affine connections, Proceedings of the Japan Academy 34 (6) (1958) 325--330.
- T. Otsuki, On general connections I, Mathematical Journal of Okayama University 9 (1960) 99--164.
- T. Otsuki, On general connections II, Mathematical Journal of Okayama University 10 (1961) 113--124.
- T. Otsuki, On metric general connections, Proceedings of the Japan Academy 37 (1961) 183--188.
- Dj. F. Nadj, The Frenet formula of Riemann-Otsuki space, Review of Research Faculty of Science University of Novi Sad Mathematics Series 16 (1) (1986) 95--106.
- Dj. F. Nadj, The Gauss, Codazzi and Kühne equations of Riemann-Otsuki spaces, Acta Mathematica Hungarica 44 (3-4) (1984) 255--260.
- A. Moor, Otsukische übertragung mit rekurrentem masstensor, Acta Scientiarum Mathematicarum 40 (1-2) (1978) 129--142.
- A. Moor, Über die veränderung der länge der vektoren in Weyl-Otsukischen räumen, Acta Scientiarum Mathematicarum 41 (1-2) (1979) 173--185.
- B. Pirinççi, Congruence of curves in Weyl-Otsuki spaces, Adıyaman University Journal of Science 14 (2) (2024) 123--139.