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## Relatively normal-slant helices lying on a surface and their characterizations

#### Nesibe MACİT [1] , Mustafa DÜLDÜL [2]

In this paper, we consider a regular curve on an oriented surface in Euclidean 3-space with the Darboux frame $\{T,U,V\}$ along the curve,
where $T$ is the unit tangent vector field of the curve, $U$ is the surface normal restricted to the curve and $V=T\times U$. We define a new curve on a surface by using the Darboux frame. This new curve whose vector field V makes a constant angle with a fixed direction is called as
relatively normal-slant helix. We give some characterizations for such curves and obtain their axis. Besides we give some relations between
some special curves (general helices, integral curves, etc.) and relatively normal-slant helices. Moreover, when a regular surface is given
by its implicit or parametric equation, we introduce the method for generating the relatively normal-slant helix with the chosen direction and constant angle on the given surface.
Slant helix, generalized helix, Darboux frame, implicit surface, parametric surface, spherical indicatrix
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Birincil Dil en Matematik Matematik Yazar: Nesibe MACİT Yazar: Mustafa DÜLDÜL (Sorumlu Yazar) Yayımlanma Tarihi : 1 Haziran 2017
 Bibtex @araştırma makalesi { hujms450971, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2017}, volume = {46}, pages = {397 - 408}, doi = {}, title = {Relatively normal-slant helices lying on a surface and their characterizations}, key = {cite}, author = {MACİT, Nesibe and DÜLDÜL, Mustafa} } APA MACİT, N , DÜLDÜL, M . (2017). Relatively normal-slant helices lying on a surface and their characterizations. Hacettepe Journal of Mathematics and Statistics , 46 (3) , 397-408 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/38758/450971 MLA MACİT, N , DÜLDÜL, M . "Relatively normal-slant helices lying on a surface and their characterizations". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 397-408 Chicago MACİT, N , DÜLDÜL, M . "Relatively normal-slant helices lying on a surface and their characterizations". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 397-408 RIS TY - JOUR T1 - Relatively normal-slant helices lying on a surface and their characterizations AU - Nesibe MACİT , Mustafa DÜLDÜL Y1 - 2017 PY - 2017 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 397 EP - 408 VL - 46 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Relatively normal-slant helices lying on a surface and their characterizations %A Nesibe MACİT , Mustafa DÜLDÜL %T Relatively normal-slant helices lying on a surface and their characterizations %D 2017 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 46 %N 3 %R %U ISNAD MACİT, Nesibe , DÜLDÜL, Mustafa . "Relatively normal-slant helices lying on a surface and their characterizations". Hacettepe Journal of Mathematics and Statistics 46 / 3 (Haziran 2017): 397-408 . AMA MACİT N , DÜLDÜL M . Relatively normal-slant helices lying on a surface and their characterizations. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 397-408. Vancouver MACİT N , DÜLDÜL M . Relatively normal-slant helices lying on a surface and their characterizations. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 408-397.