Pure and Applied Mathematics Journal

Volume 4, Issue 1, January 2015

  • Terquem Theorem with the Spherical Helix Strip

    Filiz Ertem Kaya

    Issue: Volume 4, Issue 1-2, January 2015
    Pages: 1-5
    Received: 23 October 2014
    Accepted: 25 October 2014
    Published: 11 January 2015
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    This article belongs to the Special Issue Applications of Geometry
    Abstract: The spherical helix and the strip are respectively proved firstly by Scofield and Sabuncuoglu and Hacısalihoglu. In this paper helix strip on sphere is investigated by using characteristics of spherical helix and strip. Firstly using strip after helixand finally spherical helix. So spherical helix strips are obtained. Furhermore Joachimsthal Theor... Show More
  • On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space

    Filiz Ertem Kaya

    Issue: Volume 4, Issue 1-2, January 2015
    Pages: 6-9
    Received: 8 November 2014
    Accepted: 12 November 2014
    Published: 12 January 2015
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    This article belongs to the Special Issue Applications of Geometry
    Abstract: In this paper, the involute and evolute of the curve is studied in type of the curve-surface pair at first time. In additional whenβ is considered evolute and involute of the curveα, involute and evolute curve-surface pairs (called as strip) and strip of the curveαis shown as(α,M) are given with depending on the constant angleφthat is between in an... Show More
  • Connection Forms of an Orthonormal Frame Field in the Minkowski Space

    Keziban Orbay

    Issue: Volume 4, Issue 1-2, January 2015
    Pages: 10-13
    Received: 13 October 2014
    Accepted: 10 November 2014
    Published: 12 January 2015
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    This article belongs to the Special Issue Applications of Geometry
    Abstract: In this work, connection formulas and forms of an orthonormal frame field in the Minkowski space were introduced and then the variation of connection forms was studied. In addition, the relation between the matrix of connection forms and the transition matrix of an orthonormal basis of tangent space were established, and an example was illustrated... Show More
  • On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection

    Aysel Turgut Vanli, Ramazan Sari

    Issue: Volume 4, Issue 1-2, January 2015
    Pages: 14-18
    Received: 14 November 2014
    Accepted: 20 November 2014
    Published: 12 January 2015
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    This article belongs to the Special Issue Applications of Geometry
    Abstract: In this paper, semi-invariant submanifolds of a generalized Kenmotsu manifold endowed with a semi-symmetric non-metric connection are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be semi-invarinat submanifold with semi-symmetric non-metric connection. Morever, we studied the integrabi... Show More
  • On the Explicit Parametric Equation of a General Helix with First and Second Curvature in Nil 3-Space

    Şeyda Kılıçoğlu

    Issue: Volume 4, Issue 1-2, January 2015
    Pages: 19-23
    Received: 21 November 2014
    Accepted: 24 November 2014
    Published: 12 January 2015
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    This article belongs to the Special Issue Applications of Geometry
    Abstract: Nil geometry is one of the eight geometries of Thurston's conjecture. In this paper we study in Nil 3-space and the Nil metric with respect to the standard coordinates (x,y,z) is gNil₃=(dx)²+(dy)²+(dz-xdy)² in IR³. In this paper, we find out the explicit parametric equation of a general helix. Further, we write the explicit equations Frenet vector ... Show More
  • Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space

    Ayşe Yavuz, F. Nejat Ekmekci

    Issue: Volume 4, Issue 1-2, January 2015
    Pages: 24-27
    Received: 26 November 2014
    Accepted: 4 December 2014
    Published: 12 January 2015
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    This article belongs to the Special Issue Applications of Geometry
    Abstract: In this paper generalized Gaussian and mean curvatures of a parallel hypersurface in E^(n+1) Euclidean space will be denoted respectively by K ̅ and H ̅, and Generalized Gaussian and mean curvatures of a parallel hypersurface in E₁ⁿ⁺¹ Lorentz space will be denoted respectively by K ̿ and H ̿.Generalized Gaussian curvature and mean curvatures, K ̅an... Show More
  • Generalized Nörlund Summability of Fuzzy Real Numbers

    Adem Eroglu, Saban Yilmaz

    Issue: Volume 4, Issue 1-2, January 2015
    Pages: 28-30
    Received: 9 December 2014
    Accepted: 23 December 2014
    Published: 12 January 2015
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    This article belongs to the Special Issue Applications of Geometry
    Abstract: Fuzzy set, mathematical modelling in order to some uncertainty in 1965 was described by L. A. Zadeh [7]. In studies on fuzzy sets, fuzzy numbers [5], fuzzy relations [5], fuzzy function [5], fuzzy sequence [4] is defined as concepts. After Nörlund fuzzy and blurry Riez summability have been identified [6]. In this study, fuzzy Generalized Nörlund s... Show More
  • On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor

    Mehmet Atçeken, Umit Yildirim

    Issue: Volume 4, Issue 1-2, January 2015
    Pages: 31-34
    Received: 10 March 2015
    Accepted: 18 March 2015
    Published: 11 April 2015
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    This article belongs to the Special Issue Applications of Geometry
    Abstract: We classify almost C(α)-manifolds, which satisfy the curvature conditions (Z ) ̃(ξ,X)R=0, (Z ) ̃(ξ,X) (Z ) ̃=0, (Z ) ̃(ξ,X)S=0 and (Z ) ̃(ξ,X)P=0, where (Z ) ̃ is the concircular curvature tensor, P is the Weyl projective curvature tensor, S is the Ricci tensor and R is Riemannian curvature tensor of manifold.