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

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