Original scientific paper

$V_{n}$-slant helices in Euclidean $n$-space $E^{n}$

İsmail Gök ; Department of Mathematics, Faculty of Science, University of Ankara, 06 100 Tandoğan-Ankara, Turkey
Çetin Camci ; Department of Mathematics, Art and Science Faculty, Çanakkale Onsekiz Mart University, Çanakkale-17100, Turkey
Hilmi Hacisalihoğlu ; Department of Mathematics, Faculty of Science, University of Ankara, 06 100 Tandoğan-Ankara, Turkey

Abstract

In this paper, we give a definition of harmonic curvature functions in terms of $V_{n}$ and we define a new kind of a slant helix. We call this new slant helix a $V_{n}$-slant helix in $n$-dimensional Euclidean space $E^{n}$ and define it by using new harmonic curvature functions. We also define a vector field $D$ which we call a Darboux vector field of a $V_{n}$-slant helix in $n$-dimensional Euclidean space $E^{n}$ and we give a new characterization as:
\begin{equation*}
\text{\textquotedblleft }\alpha :I\subset
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\longrightarrow E^{n}\text{ is a }V_{n}\text{-slant helix }\Leftrightarrow
H_{n-2}^{\ast ^{\prime }}-k_{1}H_{n-3}^{\ast }=0\text{\textquotedblright},
\end{equation*}%
where $H_{n-2}^{\ast },H_{n-3}^{\ast }$ are harmonic curvature functions and
$k_{1}$ shows the first curvature function of the curve $\alpha $.

Keywords

slant helices; harmonic curvature functions; Euclidean n-space

Hrčak ID:

44018

URI

https://hrcak.srce.hr/44018

Publication date:

9.12.2009.

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