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Terquem Theorem with the Spherical Helix Strip
Issue:
Volume 4, Issue 1-2, January 2015
Pages:
1-5
Received:
23 October 2014
Accepted:
25 October 2014
Published:
11 January 2015
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 Theorem and Terquem Theorem are investigated when the strip and helix strips which lie on the sphere and given a characterization about spherical helix strips.
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...
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On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space
Issue:
Volume 4, Issue 1-2, January 2015
Pages:
6-9
Received:
8 November 2014
Accepted:
12 November 2014
Published:
12 January 2015
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 and in Euclidean 3-Space E^3.
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...
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Connection Forms of an Orthonormal Frame Field in the Minkowski Space
Issue:
Volume 4, Issue 1-2, January 2015
Pages:
10-13
Received:
13 October 2014
Accepted:
10 November 2014
Published:
12 January 2015
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.
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...
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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
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 integrability condition of the distribution on semi-invariant submanifolds of generalized Kenmotsu manifold with semi-symmetric non-metric connection.
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...
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On the Explicit Parametric Equation of a General Helix with First and Second Curvature in Nil 3-Space
Issue:
Volume 4, Issue 1-2, January 2015
Pages:
19-23
Received:
21 November 2014
Accepted:
24 November 2014
Published:
12 January 2015
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 fields, the first and the second curvatures of general helix in Nil 3-Space. The parametric equation the Normal and Binormal ruled surface of general helix in Nil 3-space in terms of their curvature and torsion has been already examined in [12], in Nil 3-Space.
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 ...
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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
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 ̅and H ̅ofaparallel hypersurface in E^(n+1)Euclidean space are givenin[2].Before nowwe studied relations between curvatures of a hypersurface in Lorentzian space and we introduced higher order Gaussian curvatures of hypersurfaces in Lorentzian space. In this paper, by considering our last studieson higher order Gaussian and mean curvatures, we calculate the generalized K ̿and H ̿ofaparallel hypersurface in E₁ⁿ⁺¹ Lorentz space and we prove theorems about generalized K ̿and H ̿ ofa parallel hypersurface in E₁ⁿ⁺¹ Lorentz space.
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...
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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
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 summability have been defined and Generalized Nörlund summability necessary and sufficient conditions to ensure the regular was investigated.
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...
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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
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.
