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Öğe On Jacobi's theorems(Communications Series A1: Mathematics and Statistics, 1998) Karadağ, H. Bayram; Keleş, SadıkÖz (İngilizce): In this paper, J. Jacobi's Theorems [9] have been considered for the spherical curves drawn on the unit dual sphere during the closed space motions. The integral invariants of the ruled surface corresponding, in the line space, to the spherical curve drawn by a fixed point on the moving unit dual sphere during the one-parameter closed motion were calculated with a different approach from the area vector used by H. R. Müller [11]. In addition, the ruled surfaces corresponding to the curves drawn by the unit tangent vector, principal normal vector or a unit vector on the osculating plane of the mentioned curve, were seen to be cones with this approach.Öğe Parallel projection area and Holditch's theorem(Communications Series A1: Mathematics and Statistics, 1996) Karadağ, H. Bayram; Keleş, SadıkParallel projection area and Holditch's theoremÖğe The projection area in the lines space(1998) Karadağ, H. Bayram; Keleş, Sadık[Abstract Not Acailable]Öğe QR-submanifolds and almost contact 3-structure(Turkish Journal of Mathematics, 2000) Güneş, Rıfat; Şahin, Bayram; Keleş, SadıkYıl: 2000Cilt: 24Sayı: 3ISSN: 1300-0098Sayfa Aralığı: 239 - 250 Metin Dili: İngilizce Öz: Başlık (İngilizce): Öz (İngilizce): In this paper,QR-submanifolds of quaternion Kaehlerian manifolds with dim?? = 1 has been considered. It is shown that each QR-submanifold of quaternion Kaehlerian manifold with dim?? is a manifold with an almost contact 3-structure. We apply geometric theory of almost contact 3-structure to the classification of QR-submanifolds (resp.Real hypersurfaces) of quaternion Kaehler manifolds (resp.IR4m, m > 1). Some results on integrability of an invariant distribution of a QR-submanifold and on the immersions of its leaves are also obtained.Öğe Schouten and Vr?anceanu Connections on Golden Manifolds(2019) Gök, Mustafa; Keleş, Sadık; Kılıç, ErolIn this paper, we study two special linear connections, which are called Schouten and Vr?anceanuconnections, defined by an arbitrary fixed linear connection on a differentiable manifoldadmitting a golden structure. The golden structure defines two naturally complementary projectionoperators splitting the tangent bundle into two complementary parts, so there are two globallycomplementary distributions of the tangent bundle. We examine the conditions of parallelismfor both of the distributions with respect to the fixed linear connection under the assumptionthat it is either the Levi-Civita connection or is not. We investigate the concepts of halfparallelism and anti half parallelism for each of the distributions with respect to the Schoutenand Vr?anceanu connections. We research integrability conditions of the golden structure and itsassociated distributions from the viewpoint of the Schouten and Vr?anceanu connections. Finally,we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vr?anceanuconnections.Öğe Schouten and Vranceanu Connections on Golden Manifolds(International Electronic Journal of Geometry, 2019) Gök, Mustafa; Keleş, Sadık; Kılıç, ErolÖz:In this paper, we study two special linear connections, which are called Schouten and Vr˘anceanu connections, defined by an arbitrary fixed linear connection on a differentiable manifold admitting a golden structure. The golden structure defines two naturally complementary projection operators splitting the tangent bundle into two complementary parts, so there are two globally complementary distributions of the tangent bundle. We examine the conditions of parallelism for both of the distributions with respect to the fixed linear connection under the assumption that it is either the Levi-Civita connection or is not. We investigate the concepts of half parallelism and anti half parallelism for each of the distributions with respect to the Schouten and Vr˘anceanu connections. We research integrability conditions of the golden structure and its associated distributions from the viewpoint of the Schouten and Vr˘anceanu connections. Finally, we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vr˘anceanu connections.Öğe Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces(International Electronic Journal of Geometry, 2019) Gülbahar, Mehmet; Kılı, Erol; Keleş, SadıkÖz: Riemannian submersions between Lie groups and Riemannian homogeneous spaces are investigated. With the help of connections, some characterizations dealing these spaces are obtained.Öğe ? -submanifolds of para-Sasakian manifolds(Turkish Journal of Mathematics, 2014) Yuksel, Selcen Perktas; Trıpathı, Mukut Mani; Kılıç, Erol; Keleş, SadıkAbstract: Almost semiinvariant ξ ⊥ -submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant ξ ⊥ -submanifolds and semiinvariant ξ ⊥ -submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant ξ ⊥ -submanifold of a normal almost paracontact metric (and hence para-Sasakian) manifold with the proper invariant distribution always possesses a para-CR-structure. A counter example is also given. Integrability conditions for certain natural distributions arising on almost semiinvariant ξ ⊥ -submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.Öğe ξ ⊥ -submanifolds of para-Sasakian manifolds(2014) Perktaş Yüksel, Selcan; Trıpathı, Mukut Mani; Kılıç, Erol; Keleş, Sadık
