Open AccessOn k-type spacelike slant helices lying on lightlike surfaces
Author(s) -
Ufuk Öztürk,
Emilija Nešović,
Öztürk Koç Esra
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1909781o
Subject(s) - mathematics , torsion (gastropod) , geodesic , principal curvature , minkowski space , frenet–serret formulas , curvature , lying , mathematical analysis , surface (topology) , type (biology) , differential geometry , geometry , pure mathematics , mathematical physics , mean curvature , medicine , ecology , surgery , biology , radiology
In this paper, we define k-type spacelike slant helices lying on a lightlike surface in Minkowski space E31 according to their Darboux frame for k ? {0,1,2}. We obtain the necessary and the sufficient conditions for spacelike curves with non-null and null principal normal lying on lightlike surface to be the k-type spacelike slant helices in terms of their geodesic curvature, normal curvature and geodesic torsion. Additionally, we determine their axes and show that the Darboux frame of a spacelike curve lying on a lightlike surface coincides with its Bishop frame if and only if it has zero geodesic torsion. Finally, we give some examples.