The aim of this paper is to introduce inclined curves according to parallel transport frame. This paper begins by defined a vector field $D$ called Darboux vector field of an inclined curve in $E^{4}$. It will then go on to an alternative characterization for the inclined curves
$\alpha :I\subset \mathbb{R} \longrightarrow E^{4}\text{ is an inclined curve}\Leftrightarrow k_{1}(s)\int k_{1}(s)ds+k_{2}(s)\int k_{2}(s)ds+k_{3}(s)\int k_{3}(s)ds=0 $
where $k_{1}(s)$, $k_{2}(s),$ $k_{3}(s)$ are the principal curvature functions according to parallel transport frame of the curve $\alpha $ and also, similar characterization for the generalized helices according to Bishop frame in $E^{3}$ is given by
$\alpha :I\subset \mathbb{R} \longrightarrow E^{3}\text{ is a generalized helix}\Leftrightarrow k_{1}(s)\int k_{1}(s)ds+k_{2}(s)\int k_{2}(s)ds=0 $
where $k_{1}(s)$, $k_{2}(s)$ are the principal curvature functions according to Bishop frame of the curve $\alpha $. These curves have illustrated some examples and draw their figures with use of Mathematica programming language. Also, it is given an example for the inclined curve in $E^{4}$ and showed that the above condition is satisfied for this curve.
Primary Language  tr 

Subjects  Engineering 
Journal Section  Articles 
Authors 

Dates 
Publication Date: April 15, 2019 
Bibtex  @research article { konuralpjournalmath525932,
journal = {Konuralp Journal of Mathematics (KJM)},
issn = {},
eissn = {2147625X},
address = {Mehmet Zeki SARIKAYA},
year = {2019},
volume = {7},
pages = {16  24},
doi = {},
title = {Characterizations of Inclined Curves According to Parallel Transport Frame in \$E\^\{4\}\$ and Bishop Frame in \$E\^\{3\}\$},
key = {cite},
author = {Ateş, Fatma and Gok, İsmail and Ekmekci, Faik nejat and Yaylı, Yusuf}
} 
APA  Ateş, F , Gok, İ , Ekmekci, F , Yaylı, Y . (2019). Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$. Konuralp Journal of Mathematics (KJM), 7 (1), 1624. Retrieved from http://dergipark.org.tr/konuralpjournalmath/issue/31492/525932 
MLA  Ateş, F , Gok, İ , Ekmekci, F , Yaylı, Y . "Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$". Konuralp Journal of Mathematics (KJM) 7 (2019): 1624 <http://dergipark.org.tr/konuralpjournalmath/issue/31492/525932> 
Chicago  Ateş, F , Gok, İ , Ekmekci, F , Yaylı, Y . "Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$". Konuralp Journal of Mathematics (KJM) 7 (2019): 1624 
RIS  TY  JOUR T1  Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$ AU  Fatma Ateş , İsmail Gok , Faik nejat Ekmekci , Yusuf Yaylı Y1  2019 PY  2019 N1  DO  T2  Konuralp Journal of Mathematics (KJM) JF  Journal JO  JOR SP  16 EP  24 VL  7 IS  1 SN  2147625X M3  UR  Y2  2019 ER  
EndNote  %0 Konuralp Journal of Mathematics (KJM) Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$ %A Fatma Ateş , İsmail Gok , Faik nejat Ekmekci , Yusuf Yaylı %T Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$ %D 2019 %J Konuralp Journal of Mathematics (KJM) %P 2147625X %V 7 %N 1 %R %U 
ISNAD  Ateş, Fatma , Gok, İsmail , Ekmekci, Faik nejat , Yaylı, Yusuf . "Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$". Konuralp Journal of Mathematics (KJM) 7 / 1 (April 2019): 1624. 
AMA  Ateş F , Gok İ , Ekmekci F , Yaylı Y . Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$. Konuralp J. Math.. 2019; 7(1): 1624. 
Vancouver  Ateş F , Gok İ , Ekmekci F , Yaylı Y . Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$. Konuralp Journal of Mathematics (KJM). 2019; 7(1): 2416. 