Characterizations of the position vector of a surface curve in Euclidean 3-space


CAMCI Ç. , KULA L., İLARSLAN K.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.19, no.3, pp.59-70, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 3
  • Publication Date: 2011
  • Title of Journal : ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Page Numbers: pp.59-70

Abstract

In this paper, we give some characterizations of position vector of a unit speed curve in a regular surface M subset of E-3 which always lies in the planes spanned by {T, Z}, {T, Y} and {Y, Z}, respectively, by using (curve-surface)-frame {T,Y,Z} instead of Frenet frame {T, N, B}. We characterize such curves in terms of the geodesic curvature k(g), normal curvature k(n) and geodesic torsion t(r). Furthermore, we give some characterization for the regular surface M by using the concept of transversality of surfaces in Euclidean 3-space.