Selcen Yüksel Perktaş

Indefinite Almost Paracontact Metric Manifolds

We introduce the concept of ()-almost paracontact manifolds, and in particular, of ()-para-Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of ()-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it cannot admit an ()-para Sasakian structure. We show that, for an ()-para Sasakian manifold, the conditions of being symmetric, semi-symmetric, or of constant sectional curvature are all identical. It is shown that a symmetric spacelike (resp., timelike) ()-para Sasakian manifold is locally isometric to a pseudohyperbolic space (resp., pseudosphere ). At last, it is proved that for an ()-para Sasakian manifold the conditions of being Ricci-semi-symmetric, Ricci-symmetric, and Einstein are all identical.

On Lightlike Geometry of Para-Sasakian Manifolds

We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtain a para-Sasakian structure on the leaves of an integrable distribution of a screen semi-invariant lightlike hypersurface.

Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection

We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an -Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor, -curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature. We give some characterizations for pseudo-projectively flat para-Sasakian manifolds.

BIHARMONIC HYPERSURFACES OF LP-SASAKIAN MANIFOLDS

Biharmonic Hypersurfaces of LP-Sasakian Manifolds 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.

Invariant lightlike submanifolds of golden semi-Riemannian manifolds

The Golden Ratio is fascinating topic that continually generated news ideas. A semi-Riemannian manifold endowed with a Golden Structure will be called a golden semi-Riemannian manifold. The main purpose of the present paper is to study the geometry of invariant lightlike submanifolds of golden semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be a metric connection.

Magnetic biharmonic curves on 3-dimensional normal almost paracontact metric manifolds

In this paper, we study magnetic biharmonic and biminimal curves on a 3-dimensional normal paracontact metric mani-fold with α, β =constant. We obtain necessary and sufficient conditions for biharmonicity and biminimality of a non-null magnetic curve, respectively. We give some characterizations for such curves defined in particular cases of a 3-dimensional normal almost paracontact metric manifold.In this paper, we study magnetic biharmonic and biminimal curves on a 3-dimensional normal paracontact metric mani-fold with α, β =constant. We obtain necessary and sufficient conditions for biharmonicity and biminimality of a non-null magnetic curve, respectively. We give some characterizations for such curves defined in particular cases of a 3-dimensional normal almost paracontact metric manifold.

A study on f-biharmonic curves in S(1,4)

In this paper, we study f−biharmonic curves as the critical points of the f−bienergy functional. We give necessary and sufficient conditions for a curve having a timelike binormal vector lying on a 4-dimensional conformally flat, quasi-conformally flat and conformally symmetric Lorentzian para-Sasakian manifold to be an f−biharmonic curve. Moreover, we introduce proper f−biharmonic curves on the Lorentzian sphere S14.In this paper, we study f−biharmonic curves as the critical points of the f−bienergy functional. We give necessary and sufficient conditions for a curve having a timelike binormal vector lying on a 4-dimensional conformally flat, quasi-conformally flat and conformally symmetric Lorentzian para-Sasakian manifold to be an f−biharmonic curve. Moreover, we introduce proper f−biharmonic curves on the Lorentzian sphere S14.

Biharmonic Frenet and non-Frenet Legendre curves in 3-dimensional normal almost paracontact metric manifolds

In the present paper we study non-null biharmonic curves in 3-dimensional normal almost paracontact metric manifolds. We give some necessary and sufficient conditions for Legendre curves in a 3-dimensional normal almost paracontact metric manifolds to be biharmonic in terms of structure functions α and β.

Biharmonic slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds

In the present paper we give some characterizations for non-null slant biharmonic Frenet curves of osculating order 3 in a 3-dimensional normal almost paracontact metric manifolds.