Transversal Lightlike Submanifolds of Metallic Semi-Riemannian Manifolds

The Metallic Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Metallic structure will be called a Metallic Riemannian manifold. The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike submanifolds and of Metallic Semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be metric connection. We also obtain characterization of transversal lightlike submanifolds of Metallic semi-Riemannian manifolds. Finally, we give an example.Comment: 18 pag

ON SEMI-INVARIANT SUBMANIFOLDS OF ALMOST COMPLEX CONTACT METRIC MANIFOLDS

In this article we study semi-invariant submanifolds of almost complexcontact metric manifolds.We defined semi-invariant submanifolds of almostcomplex contact metric manifold and we have investigated semi-invariantsubmanifolds of almost complex contact metric manifolds. We investigated necessary conditions on which a semi-submanifold of an amlmasot complex contact metric manifold is invariant or anti-invariant. We found necessary and sufficientconditions to be integrable and totally geodesic of distribution $D$defined on $M$. Also we obtained necessary and sufficient conditions to be integrable and totally geodesic of distribution $D^{\bot }$ defined on$M$\

η\eta-Ricci solitons in (ε)(\varepsilon)-almost paracontact metric manifolds

The object of this paper is to study $\eta$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds. We investigate $\eta$-Ricci solitons in the case when its potential vector field is exactly the characteristic vector field $\xi$ of the $(\varepsilon)$-almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and $(\varepsilon)$-para Sasakian manifolds admitting $\eta$-Ricci solitons. Finally we obtain some results for $\eta$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2)-tensor fields.Comment: 20 page

LIGHTLIKE HYPERSURFACES OF ALMOST NORDEN GOLDEN SEMI-RIEMANNIAN MANIFOLDS

In this paper, we give some classifications about lightlike hypersurfaces of almost Norden Golden semi-Riemannian manifolds. We show that, there is no radical anti-invariant lightlike hypersurfaces of an almost Norden Golden semi-Riemannian manifold. Also, we define invariant and screen semi-invariant lightlike hypersurface of almost Norden Golden semi-Riemannian manifolds and give examples

η-Ricci solitons in (ε)-almost paracontact metric manifolds

The object of this paper is to study η -Ricci solitons on ( ε ) -almost paracontact metric manifolds. We investigate η -Ricci solitons in the case when its potential vector field is exactly the characteristic vector field ξ of the ( ε ) -almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and ( ε )-para Sasakian manifolds admitting η-Ricci solitons. Finally we obtain some results for η -Ricci solitons on ( ε )-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2) -tensor fields