Warped product skew CR-submanifolds of Kenmotsu manifolds and their applications

In this paper, we introduce the notion of warped product skew CR-submanifolds in Kenmotsu manifolds. We obtain several results on such submanifolds. A characterization for skew CR-submanifolds is obtained. Furthermore, we establish an inequality for the squared norm of the second fundamental form of a warped product skew CR-submanifold M1 x fM? of order 1 in a Kenmotsu manifold ?M in terms of the warping function such that M1 = MT x M?, where MT, M? and M? are invariant, anti-invariant and proper slant submanifolds of ?M, respectively. Finally, some applications of our results are given.

On contact CR-submanifolds of a cosymplectic manifold

In this paper, we study the differential geometry of contact CR-submanifolds of a cosymplectic manifold. Necessary and sufficient conditions are given for a submanifold to be a contact CR-submanifold in cosymplectic manifolds and cosymplectic space forms. Finally, the induced structures on submanifolds are investigated, these structures are categorized and we discuss these results.

Totally Contact Umbilical Radical Transversal Lightlike Submanifolds Of An Almost Contact Manifold With B-Metric

In the present paper, we study the geometry of totally contact umbilical radical transversal lightlike submanifolds and totally contact umbilical CR- submanifold of an indenite Sasaki-like almost contact manifold with B-metric. We nd the necessary and sucient condition for the characterization of the induced connection to be a metric connection. Finally, we have proved that for a totally contact umbilical CR-submanifold, totally contact umbilical radical transversal lightlike submanifold is a totally geodesic radical transversal lightlike submanifold.

Geometry of hypersurfaces of a quarter symmetric non metric connection in a quasi-Sasakian manifold

The purpose of the paper is to study the notion of CR-submanifold and the existence of some structures on a hypersurface of a quarter symmetric non metric connection in a quasi-Sasakian manifold. We study the existence of a Kahler structure on $M$ and the existence of a globally metric frame $f$-structure in sence of Goldberg S.I., Yano K. We discuss the integrability of distributions on $M$ and geometry of their leaves. We have tries to relate this result with those before obtained by Goldberg V., Rosca R. devoted to Sasakian manifold and conformal connections.

CR-Submanifolds of Generalized -Space Forms

We study sectional curvature, Ricci tensor, and scalar curvature of submanifolds of generalized -space forms. Then we give an upper bound for foliate -horizontal (and vertical) CR-submanifold of a generalized -space form and an upper bound for minimal -horizontal (and vertical) CR-submanifold of a generalized -space form. Finally, we give the same results for special cases of generalized -space forms such as -space forms, generalized Sasakian space forms, Sasakian space forms, Kenmotsu space forms, cosymplectic space forms, and almost -manifolds.

On Submersion of CR-Submanifolds of l.c.q.K. Manifold

We study submersion of CR-submanifolds of an l.c.q.K. manifold. We have shown that if an almost Hermitian manifold B admits a Riemannian submersion π:M→B of a CR-submanifold M of a locally conformal quaternion Kaehler manifold M¯, then B is a locally conformal quaternion Kaehler manifold.

Warped product CR-submanifolds of LP-cosymplectic manifolds

In this paper, we study warped product CR-submanifolds of LP-cosymplectic manifolds. We have shown that the warped product of the type M = NT ? fN? does not exist, where NT and N? are invariant and anti-invariant submanifolds of an LP-cosymplectic manifold M?, respectively. Also, we have obtained a characterization result for a CR-submanifold to be locally a CR-warped product. 2010 Mathematics Subject Classifications. 53C15, 53C40, 53C42. .

CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold

In the present paper we have investigated CR-submanifold of a nearly trans-hyperbolic Sasakian manifold. We have also studied parallel distribution relating to