Browsing by Author "Kocayiǧit H."
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Item Differential equations characterizing timelike and spacelike curves of constant breadth in minkowski 3-space E3 1(2011) Önder M.; Kocayiǧit H.; Candan E.In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space E3 1. Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in E3 1. As an example, the obtained results are applied to the case ρ = const. and k2= const., and are discussed. © 2011 The Korean Mathematical Society.Item Characterizations of slant helices according to quaternionic frame(2013) Kocayiǧit H.; Betül Pekacar B.In this study, we studied some integral characterizations of slant helices according to quaternionic frame in 3and 4-dimensional Euclidean spaces E3 and E4. Furthermore, we obtain some necessary and sufficient conditions for a space curve to be a slant helix according to quaternionic frame. © 2013 Hüseyin KOCAYİǦİT and Beyza Betül PEKACAR.Item Space curves of constant breadth in Minkowski 3-space(2013) Kocayiǧit H.; Önder M.In this paper, we study spacelike and timelike curves of constant breadth in Minkowski 3-space. We show that in Minkowski 3-space spacelike and timelike curves of constant breadth are normal, helices, and spherical curves in some special cases. Furthermore, we give that the total torsion of a closed spacelike curve of constant breadth is zero while the total torsion of a simple closed timelike curve is equal to 2πn, (n ∈ Z). © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.Item Some characterizations of timelike curves according to bishop frame in minkowski 3-space(2013) Kocayiǧit H.; Özdemir A.; Çetin M.; Arda B.In this study, we give some characterizations of timelike curves according to Bishop Frame in Minkowski 3-space E13 by using Laplacian operator and Levi-Civita connection.Item Characterizations of N3 slant helices according to quaternionic frame(2014) Kocayiǧit H.; Pekacar B.B.In this study, we studied some integral characterizations of N3 slant helices according to quaternionic frame in 4-dimensional Euclidean space E4 Furthermore, we obtain some necessary and sufficient conditions for a space curve to be a N3 slant helix according to quaternionic frame. ©2014 Hüseyin Kocayiĝit and Beyza Betül Pekacar.Item Harmonic 1-type curves and weak biharmonic curves in Lorentzian 3-space(2014) Kocayiǧit H.; Önder M.; Hacisalihoǧlu H.H.In this paper, we give definitions and characterizations of harmonic 1-type and weak biharmonic curves by using the mean curvature vector field of a Frenet curve in the Lorentzian 3-space L3. We also study weak biharmonic curves whose mean curvature vector fields are in the kernel of normal Laplacian ∇⊥. We give some theorems for them in L3. Moreover, we give some characterizations and results for a Frenet curve in the same space.Item A statistical comparison of anatomical features in some ornithogalum sp. Species; [Comparação Estatística das Características Anatômicas em Espécies de Ornithogalum sp](Sociedade Brasileira da Ciencia das Plantas Daninha, 2016) Özdemir A.; Kocayiǧit H.; Yetişen K.; Akyol Y.; Özdemir C.In the present study, Ornithogalum narbonense, O. montanum, O. wiedemannii, O. sigmoideum and O. lanceolatum species were compared statistically with respect to anatomical characters. Some differences were found in root, stem and leaf anatomy of the species. These differences and similarities were indicated in this study. A big metaxylem was present in all root cross sections, except for O. lanceolatum, which has three metaxylema. 2-3 layered annular type collenchyma were present in all species. Aerenchyma is present in all mesophiles. © 2016, Sociedade Brasileira da Ciencia das Plantas Daninha. All rights reserved.Item Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold(Sciendo, 2021) Aydin T.A.; Sezer M.; Kocayiǧit H.In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined. © 2021 Tuba Aǧirman Aydin et al., published by Sciendo.Item Some New Characterizations of the Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space(Sciendo, 2021) Samanci H.K.; Ayaz S.; Kocayiǧit H.A Laplace operator and harmonic curve have very important uses in various engineering science such as quantum mechanics, wave propagation, diffusion equation for heat, and fluid flow. Additionally, the differential equation characterizations of the harmonic curves play an important role in estimating the geometric properties of these curves. Hence, this paper proposes to compute some new differential equation characterizations of the harmonic curves in Euclidean 3-space by using an alternative frame named the N-Bishop frame. Firstly, we investigated some new differential equation characterizations of the space curves due to the N-Bishop frame. Secondly, we firstly introduced some new space curves which have the harmonic and harmonic 1-type vectors due to alternative frame N-Bishop frame. Finally, we compute new differential equation characterizations using the N-Bishop Darboux and normal Darboux vectors. Thus, using these differential equation characterizations we have proved in which conditions the curve indicates a helix. © 2021 Hatice Kuşak Samanci et al., published by Sciendo.Item Some new characterizations of a space curve due to a modified frame {N →, C →, W →} in Euclidean 3-space(De Gruyter Open Ltd, 2023) Ayaz S.; Kuşak Samanci H.; Kocayiǧit H.In our paper, we computed some new characterizations due to an alternative modified frame {N →, C →, W →} in Euclidean 3-space and we get general differential equation characterizations of a space curve due to the vectors N →, C →, W →. Furthermore, we investigated some differential equations characterizations of the harmonic and harmonic 1-type curves. © 2021 Walter de Gruyter GmbH, Berlin/Boston.