In this paper, the curvature and torsion of Smarandache curves obtained by vectors Bertrand partner curve are calculated. These values expressed depending upon curve. Besides, we illustrate example with our main results.

The objective of this paper is to investigate palindromes in three Smarandache-type arithmetic functions,namely, the Smarandache function S(n), pseudo Z(n), and Sandor-Smarandache SS(n).

abstract: In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the asymptoti...

In this paper, we study the hypersurface families with Smarandache curves in 4-dimensional Galilean space G 4 and give conditions for different to be parameter curve which generates is geodesic on a . Also, investigate three types of marching-scale functions one these hypersurfaces construct an example it.

This paper finds sufficient conditions to determine a surface whose mean curvature along given Smarandache curve is constant in three-dimensional Lie group. accomplished by using the Frenet frames of specified express surfaces that span TN, NB, and TB curves parametrically. In terms curvatures curves, marching scale functions, their partial derivatives, these are determined. Sufficient found ma...