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Öğe Euclidean curves with incompressible canonical vector field(2018) Arslan, Kadri; Aydın, Yılmaz; Demirbaş, Eray; Yazla, AzizIn the present study we consider Euclidean curves with incompressible canonicalvector fields. We investigate such curves in terms of their curvature functions. Recently,B.Y. Chen gave classification of plane curves with incompressible canonical vectorfields. For higher dimensional case we gave a complete classification of Euclideanspace curves with incompressible canonical vector fields. Further we obtain someresults of the Euclidean curves with incompressible canonical vector fields in 4 -dimensional Euclidean space E4Öğe H-Recurrent surfaces in Euclidean space Em(Selcuk University Research Center of Applied Mathematics, 2011) Arslan, Kadri; Murathan, Cengizhan; Özturk, Günay; Türkay, SelenThe object of the paper is to study some smooth surfaces M whose mean curvature vector H satisfies the H-recurrent condition D_{X}H=?(X)H in m-dimensional Euclidean space E^{m}, where X is a tangent vector field of M and ? is a 1-form. First of all,we prove that the surfaces which satisfy the H-recurrent condition in E^{m} are R^{?}-parallel (i.e., R^{?}H=0). Then, we show that H-parallel surfaces in E? are either totally umbilical or normally flat.
