Yazar "Ilarslan, K." seçeneğine göre listele

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    Öğe
    Characterizations of slant helices in Euclidean 3-space
    (Scientific Technical Research Council Turkey-Tubitak, 2010) Kula, L.; Ekmekci, N.; Yayli, Y.; Ilarslan, K.
    In this paper we investigate the relations between a general helix and a slant helix. Moreover, we obtain some differential equations which they are characterizations for a. space curve to be a slant helix. Also, we obtain the slant helix equations and its Frenet aparatus.
  • [ X ]
    Öğe
    New approach to timelike Bertrand curves in 3-dimensional Minkowski space
    (Vasyl Stefanyk Precarpathian Natl Univ, 2023) Erdem, H. A.; Ucum, A.; Ilarslan, K.; Camci, C.
    In the theory of curves in Euclidean 3-space, it is well known that a curve /3 is said to be a Bertrand curve if for another curve /3* there exists a one-to-one correspondence between /3 and /3* such that both curves have common principal normal line. These curves have been studied in differ-ent spaces over a long period of time and found wide application in different areas. In this article, the conditions for a timelike curve to be Bertrand curve are obtained by using a new approach in contrast to the well-known classical approach for Bertrand curves in Minkowski 3-space. Related examples that meet these conditions are given. Moreover, thanks to this new approach, timelike, spacelike and Cartan null Bertrand mates of a timelike general helix have been obtained.
  • [ X ]
    Öğe
    ON THE EXPLICIT CHARACTERIZATION OF CURVES ON A (n - 1)-SPHERE IN Sn
    (Int Electronic Journal Geometry, 2013) Camci, C.; Kula, L.; Ilarslan, K.; Hacisalihoglu, H. H.
    In (n+1)-dimensional Euclidean space E-n+(1), harmonic curvatures and focal curvatures of a non-degenerate curve were defined by Ozdamar and Hacisalihoglu in [7] and by Uribe-Vargas in [9], respectively. In this paper, we investigate the relations between the harmonic curvatures of a non-degenerate curve and the focal curvatures of tangent indicatrix of the curve. Also we give the relationship between the Frenet apparatus (vectors and the curvature functions) of a curve alpha in E-n (+1) and the Frenet apparatus of tangent indicatrix alpha(T) of the curve alpha. In the main theorem of the paper, we give a characterization for a curve to be a (n-1)-spherical curve in S-n by using focal curvatures of the curve. Furtermore we give that harmonic curvature of the curve is focal curvature of the tangent indicatrix.