Some Characterizations of Cylindrical Helices in E
نویسندگان
چکیده
We consider a unit speed curve α in Euclidean n-dimensional space E n and denote the Frenet frame by {V 1 ,. .. , V n }. We say that α is a cylindrical helix if its tangent vector V 1 makes a constant angle with a fixed direction U. In this work we give different characterizations of such curves in terms of their curvatures.
منابع مشابه
Generalization of general helices and slant helices
In this work, we use the formal definition of $k$-slant helix cite{ali2} to obtain the intrinsic equations as well as the position vector for emph{slant-slant helices} which a generalization of emph{general helices} and emph{slant helices}. Also, we present some characterizations theorems for $k$-slant helices and derived, in general form, the intrinsic equations for such curves. Thereafter, fr...
متن کاملSome Characterizations of Slant Helices in the Euclidean Space E
In this work, the notion of a slant helix is extended to the space E. First, we introduce the type-2 harmonic curvatures of a regular curve. Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some c...
متن کاملASSOCIATED CURVES OF THE SPACELIKE CURVE VIA THE BISHOP FRAME OF TYPE-2 IN E₁³
The objective of the study in this paper is to define M₁,M₂-direction curves and M₁,M₂-donor curves of the spacelike curve γ via the Bishop frame of type-2 in E₁³. We obtained the necessary and sufficient conditions when the associated curves to be slant helices and general helices via the Bishop frame of type-2 in E₁³. After defining the spherical indicatrices of the associated curves, we obta...
متن کاملSome Characterizations of Special Curves in the Euclidean Space E
In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented.
متن کاملB-FOCAL CURVES OF BIHARMONIC B-GENERAL HELICES IN Heis
In this paper, we study B-focal curves of biharmonic B -general helices according to Bishop frame in the Heisenberg group Heis Finally, we characterize the B-focal curves of biharmonic B- general helices in terms of Bishop frame in the Heisenberg group Heis
متن کامل