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Öğe Anti-invariant submanifolds of locally decomposable golden Riemannian manifolds(Balkan Society of Geometers, 2020) Gök M.; Kiliç E.; Keleş S.In this paper, we give some properties of anti-invariant submanifolds of a golden Riemannian manifold. We obtain some necessary conditions for any submanifold in a locally decomposable golden Riemannian manifold to be anti-invariant. In these conditions, we also show that the submanifold is totally geodesic. We find a local orthonormal frame for the normal bundle of any anti-invariant submanifold of a locally decomposable golden Riemannian manifold. Finally, we demonstrate the existence of unit and mutually orthogonal normal vector fields such that their corresponding second fundamental tensors vanish identically under the assumption that the codimension of the anti-invariant submanifold is greater than its dimension. © Balkan Society of Geometers, Geometry Balkan Press 2020.Öğe Biharmonic hypersurfaces of LP-Sasakian manifolds(Universitatii Al.I.Cuza din Iasi, 2011) Perkta S.Y.; Kiliç E.; Keleş S.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.Öğe Closed spherical motions and Holditch's theorem(1994) Günş R.; Keleş S.In this paper, the relation between the Steiner vector of a one-parameter closed spherical motion and the area vector of the closed spherical curve formed under the motion is discussed and some corollaries are given. Moreover, making use of the area formula of W. Blaschke and the area vector defined by H. R. Müller, the formula given by H. H. Hacisaliho?lu is obtained by a different method. © 1994.Öğe Hypersurfaces of lorentzian para-sasakian manifolds(Mathematica Scandinavica, 2011) Perktaş S.; Kiliç E.; Keleş S.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 (1, 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 noninvariant hypersurface of aLorentzian 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.Öğe Notes on degenerate curves in pseudo-Euclidean spaces of index two(2012) Göçmen M.; Keleş S.In this paper, we deal with curves with degeneration degree two in pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the 6-dimensional pseudo-Euclidean space of index two. Also, we characterize pseudo-spherical null curves in the n-dimensional pseudo-Euclidean space of index two in terms of the curvature functions. © 2012 Pushpa Publishing House.Öğe Some inequalities on screen homothetic lightlike hypersurfaces of a Lorentzian manifold(2013) Gülbahar M.; Kiliç E.; Keleş S.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 ?(n1,..., nk)-invariant and some characterizations (totally umbilicity, totally geodesicity, minimality, etc.) for lightlike hypersurfaces.
