{"title":"Some Characterizations of Isotropic Curves In the Euclidean Space","authors":"S\u00fcha Y\u0131lmaz, Melih Turgut","volume":19,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":489,"pagesEnd":492,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/1544","abstract":"The curves, of which the square of the distance\nbetween the two points equal to zero, are called minimal or isotropic\ncurves [4]. In this work, first, necessary and sufficient conditions to\nbe a Pseudo Helix, which is a special case of such curves, are\npresented. Thereafter, it is proven that an isotropic curve-s position\nvector and pseudo curvature satisfy a vector differential equation of\nfourth order. Additionally, In view of solution of mentioned\nequation, position vector of pseudo helices is obtained.","references":"[1] W. Blaschke and H. Reichard, Einfuhrung in die Differential Geometrie,\nBerlin-Gottingen-Heidelberg, 1960.\n[2] C. Boyer, A History of Mathematics, New York: Wiley,1968.\n[3] U. Pekmen, \"On Minimal Space Curves in the Sense of Bertrand\nCurves\", Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Vol.10, pp.\n3-8 ,1999.\n[4] F. Semin, Differential Geometry I, Istanbul University, Science Faculty\nPress, 1983.\n[5] D. Struik, Lectures on Classical Differential Geometry I, America, 1961.\n[6] S. Yilmaz, S. Nizamoglu and M. Turgut, \"A Note on Differential\nGeometry of the Curves in E4 \", Int. J. Math. Comb. Vol. 2, pp. 104-\n108, 2008.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 19, 2008"}