Yazar "Keles, Sadik" seçeneğine göre listele

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    2-DEGENERATE BERTRAND CURVES IN MINKOWSKI SPACETIME
    (Int Electronic Journal Geometry, 2012) Gocmen, Mehmet; Keles, Sadik
    In this paper we define a new type of 2-degenerate Cartan curves in Minkowski spacetime (R-1(4)). We prove that this type of curves contain only the polynomial functions as its components whose third derivative vanish completely. No curve with acceleration zero in R-1(4) is a 2-degenerate Cartan curve, therefore we show that the type of curves that we search for must contain polynomials of degree two among its components.
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    Biharmonic Curves in Lorentzian Para-Sasakian Manifolds
    (Malaysian Mathematical Sciences Soc, 2010) Keles, Sadik; Perktas, Selcen Yueksel; Kilic, Erol
    In this paper we give necessary and sufficient conditions for space-like and timelike curves in a conformally fiat, quasi conformally flat and conformally symmetric 4-dimensional Lorentzian Para-Sasakian (LP-Sasakian) manifold to be proper biharmonic. Also, we investigate proper biharmonic curves in the Lorentzian sphere S-1(4).
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    BIHARMONIC HYPERSURFACES OF LP-SASAKIAN MANIFOLDS
    (Alexandru Ioan Cuza Univ Press, Alexandru Ioan Cuza Univ Iasi, 2011) Perktas, Selcen Yuksel; Kilic, Erol; Keles, Sadik
    In this paper the biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds are studied. We firstly find the biharmonic equation for a hypersurface which admits the characteristic vector field of the Lorentzian para-Sasakian as the normal vector field. We show that a biharmonic spacelike hypersurface of a Lorentzian para-Sasakian manifold with constant mean curvature is minimal. The biharmonicity condition for a hypersurface of a Lorentzian para-Sasakian manifold is investigated when the characteristic vector field belongs to the tangent hyperplane of the hypersurface. We find some necessary and sufficient conditions for a timelike hypersurface of a Lorentzian para-Sasakian manifold to be proper biharmonic. The nonexistence of proper biharmonic timelike hypersurfaces with constant mean curvature in a Ricci flat Lorentzian para-Sasakian manifold is proved.
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    Einstein like (?)-para Sasakian manifolds
    (Academic Publication Council, 2013) Keles, Sadik; Kilic, Erol; Tripathi, Mukut Mani; Perktas, Selcen Yuksel
    Einstein like (epsilon)-para Sasakian manifolds are introduced. For an (epsilon)-para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar curvature of an Einstein like (epsilon)-para Sasakian manifold is obtained and it is shown that the scalar curvature in this case must satisfy certain differential equation. A necessary and sufficient condition for an (epsilon)-almost paracontact metric hypersurface of an indefinite locally Riemannian product manifold to be (epsilon)-para Sasakian is obtained and it is proved that the (epsilon)-para Sasakian hypersurface of an indefinite locally Riemannian product manifold of almost constant curvature is always Einstein like.
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    HYPERSURFACES OF LORENTZIAN PARA-SASAKIAN MANIFOLDS
    (Matematisk Inst, 2011) Perktas, Selcen Yuksel; Kilic, Erol; Keles, Sadik
    In this paper we study the invariant and noninvariant hypersurfaces of (1, 1, 1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an ( I, 1, 1) almost contact manifold admits an almost product structure. We investigate hypersurfaces of affinely cosymplectic and normal (1, 1, 1) almost contact manifolds. It is proved that a noninvariant hypersurface of a Lorentzian almost paracontact manifold is an almost product metric manifold. Some necessary and sufficient conditions have been given for a non invariant hypersurface of a Lorentzian para-Sasakian manifold to be locally product manifold. We establish a Lorentzian para-Sasakian structure for an invariant hypersurface of a Lorentzian para-Sasakian manifold. Finally we give some examples for invariant and noninvariant hypersurfaces of a Lorentzian para-Sasakian manifold.
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    Inequalities for scalar curvature of pseudo-Riemannian submanifolds
    (Elsevier Science Bv, 2017) Tripathi, Mukut Mani; Gulbahar, Mehmet; Kilic, Erol; Keles, Sadik
    Some basic inequalities, involving the scalar curvature and the mean curvature, for a pseudo-Riemannian submanifold of a pseudo-Riemannian manifold are obtained. We also find inequalities for spacelike submanifolds. Equality cases are also discussed. (C) 2016 Elsevier B.V. All rights reserved.
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    INVARIANT SUBMANIFOLDS IN GOLDEN RIEMANNIAN MANIFOLDS
    (Ankara Univ, Fac Sci, 2020) Gok, Mustafa; Keles, Sadik; Kilic, Erol
    In this paper, we study invariant submanifolds of a golden Riemannian manifold with the aid of induced structures on them by the golden structure of the ambient manifold. We demonstrate that any invariant sub-manifold in a locally decomposable golden Riemannian manifold leaves invariant the locally decomposability of the ambient manifold. We give a necessary and sufficient condition for any sub-manifold in a golden Riemannian manifold to be invariant. We obtain some necessary conditions for the totally geodesicity of invariant submanifolds. Moreover, we find some facts on invariant submanifolds. Finally, we present an example of an invariant submanifold.
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    ON A SEMI-SYMMETRIC NON-METRIC CONNECTION IN AN LP-SASAKIAN MANIFOLD
    (Int Electronic Journal Geometry, 2010) Perktas, Selcen Yuksel; Kilic, Erol; Keles, Sadik
    In this paper we study some properties of curvature tensor, projective curvature tensor, nu-Weyl projective tensor, concircular curvature tensor, conformal curvature tensor, quasi-conformal curvature tensor with respect to semi-symmetric non-metric connection in a Lorentzian para-Sasakian (briefly LP-Sasakian) manifold. It is shown that an LP-Sasakian manifold (M-n, g)(n > 3) with the semi-symmetric non-metric connection is an eta-Einstein manifold.
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    RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS
    (Int Electronic Journal Geometry, 2015) Perktas, Selcen Yuksel; Keles, Sadik
    In the present paper we study 3-dimensional normal almost paracontact metric manifolds admitting Ricci solitons and gradient Ricci solitons. We give an example of 3-dimensional normal almost paracontact metric manifold. It is shown that if in a 3-dimensional normal almost paracontact metric manifold with alpha, beta = constant the metric is Ricci soliton, where potential vector field V is collinear with the characteristic vector field xi, then the manifold is eta-Einstein. We also prove that an eta-Einstein 3-dimensional normal almost paracontact metric manifold with alpha, beta = constant and V = xi admits a Ricci soliton. Furthermore, we show that if a 3-dimensional normal almost paracontact metric manifold admits a Ricci soliton (g, xi, lambda) then the Ricci soliton is shrinking.
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    Ricci Solitons in 3-Dimensional Normal Almost Paracontact Metric Manifolds (vol 8, pg 34, 2015)
    (Int Electronic Journal Geometry, 2017) Perktas, Selcen Yuksel; Keles, Sadik
    The authors would like to correct some errors which appear in the orginal publication of the article Ricci Solitons in 3-Dimensional Normal Almost Paracontact Metric Manifolds [Int. Electron. J. Geom., Vol. 8, No: 2, 2015, 34-45.].
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    Schouten and Vranceanu Connections on Golden Manifolds
    (Int Electronic Journal Geometry, 2019) Gok, Mustafa; Keles, Sadik; Kilic, Erol
    In this paper, we study two special linear connections, which are called Schouten and Vranceanu 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 Vranceanu connections. We research integrability conditions of the golden structure and its associated distributions from the viewpoint of the Schouten and Vranceanu connections. Finally, we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vranceanu connections.
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    SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS
    (Int Electronic Journal Geometry, 2011) Kilic, Erol; Sahin, Bayram; Keles, Sadik
    In this paper, we introduce a new class of ligtlike submanifold called screen semi- invariant (SSI) lightlike submanifolds of a semi Riemannian product manifold. We give examples of such submanifolds and study the geometry of leaves of distributions which are involved in the definition of SSI-lightlike submanifolds. We obtain, necessary and sufficient conditions for the SSI-lightlike submanifold to be locally product manifold. Finally, we give some characterizations for totally umbilical SSI-lightlike and screen anti-invariant lightlike submanifolds of semi-Riemannian product manifolds.
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    Slant submanifolds of Kaehler product manifolds
    (Tubitak Scientific & Technological Research Council Turkey, 2007) Sahin, Bayram; Keles, Sadik
    In this paper, we study slant submanifolds of a Kaehler product manifold. We show that an F-invariant slant submanifold of Kaehler product manifold is a product manifold. We also obtain some curvature inequalities in terms of scalar curvature and Ricci tensor.
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    Some Characterizations of Semi-Invariant Submanifolds of Golden Riemannian Manifolds
    (Mdpi, 2019) Gok, Mustafa; Keles, Sadik; Kilic, Erol
    In this paper, we study some characterizations for any submanifold of a golden Riemannian manifold to be semi-invariant in terms of canonical structures on the submanifold, induced by the golden structure of the ambient manifold. Besides, we determine forms of the distributions involved in the characterizations of a semi-invariant submanifold on both its tangent and normal bundles.
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    SOME INEQUALITIES ON SCREEN HOMOTHETIC LIGHTLIKE HYPERSURFACES OF A LORENTZIAN MANIFOLD
    (Mathematical Soc Rep China, 2013) Gulbahar, Mehmet; Kilic, Erol; Keles, Sadik
    In this paper, we establish some inequalities involving k-Ricci curvature, k-scalar curvature, the screen scalar curvature on a screen homothetic lightlike hypersurface of a Lorentzian manifold. We compute Chen-Ricci inequality and Chen inequality on a screen homothetic lightlike hypersurface of a Lorentzian manifold. We give an optimal inequality involving the delta(n(1), ... , n(k))-invariant and some characterizations (totally umbilicity, totally geodesicity, minimality, etc.) for lightlike hypersurfaces.
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    ??-submanifolds of para-Sasakian manifolds
    (Tubitak Scientific & Technological Research Council Turkey, 2014) Yuksel Perktas, Selcen; Tripathi, Mukut Mani; Kilic, Erol; Keles, Sadik
    Almost semiinvariant xi(perpendicular to)-submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant xi(perpendicular to)-submanifolds and semiinvariant xi(perpendicular to)-submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant xi(perpendicular to)-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 xi(perpendicular to)-submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.
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    A USEFUL ORTHONORMAL BASIS ON BI-SLANT SUBMANIFOLDS OF ALMOST HERMITIAN MANIFOLDS
    (Tamkang Univ, 2016) Gulbahar, Mehmet; Kilic, Erol; Keles, Sadik
    In this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen's main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form.
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    Warped product submanifolds of Lorentzian paracosymplectic manifolds
    (Springer Heidelberg, 2012) Perktas, Selcen Yuksel; Kilic, Erol; Keles, Sadik
    In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form M = M-inverted perpendicular x (f) M-perpendicular to of a Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to M is a usual Riemannian product manifold where totally geodesic and totally umbilical submanifolds of warped product are invariant and anti-invariant, respectively. We prove that the distributions involved in the definition of a warped product semi-invariant submanifold are always integrable. A necessary and sufficient condition for a semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be warped product semi-invariant submanifold is obtained. We also investigate the existence and nonexistence of warped product semi-slant and warped product anti-slant submanifolds in a Lorentzian paracosymplectic manifold.