On k-type spacelike slant helices lying on lightlike surfaces | Zendy

Ufuk Öztürk | Zendy; Emilija Nešović | Zendy; Öztürk Koç | Zendy

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On k-type spacelike slant helices lying on lightlike surfaces

Author(s) -

Ufuk Öztürk,

Emilija Nešović,

Öztürk Koç

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 , mathematical analysis , lying , type (biology) , mathematical physics , surface (topology) , pure mathematics , geometry , 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.

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