In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds.
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After brief introduction, we prove that a totally contact umbilical CR-lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product.
We define a semi-symmetric non-metric connection in a nearly Sasakian manifold and we consider semi-invariant submanifolds of a nearly Sasakian manifold endowed with a semi-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.
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In this paper we introduce the notion of semi-invariant submanifolds of a Lorentzian almost contact manifold. We study their principal characteristics and the particular cases in which the manifold is a Lorentzian Sasakian manifold or a Lorentzian Sasakian space form.
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The object of the present paper is to study a transformation called D-homothetic deformation of trans-Sasakian structure. Among others it is shown that in a trans-Sasakian manifold, the Ricci operator Q does not commute with the structure tensor phi and the operator Qphi - phiQ is conformal under a D-homothetic deformation. Also the phi-sectional curvature of a trans-Sasakian manifold is conformal under such a deformation. Some non-trivial examples of trans-Sasakian (non-Sasakian) manifolds with global vector fields are obtained.
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In the present paper we have investigated CR-submanifold of a nearly trans- hyperbolic Sasakian manifold. We have also studied parallel distribution relating to vertical CR-submanifold of a nearly trans- hyperbolic Sasakian manifold.
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We define and study both screen QR-lightlike and screen CR-lightlike submanifolds of an indefinite quaternion Kaehler manifold. We show that screen QR-lightlike submanifolds include quaternion submanifolds and screen CR-lightlike submanifolds include quaternion as well as screen real lightlike submanifolds. We also give some examples of screen QR-lightlike and screen CR-lightlike submanifolds.
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Transversal hypersurfaces of Lorentzian almost paracontact manifolds are studied. It is proved that transversal hypersurfaces of Lorentzian almost paracontact manifolds admit an almost product structure and almost product Lorentzian metric structure. We shall also derive a formula which gives the relation between the connection with respect to the Lorentzian metric g and that with respect to induced Lorentzian metric G. Some properties of Lorentzian (f, g, u, v, lambda)-structure, transversal hypersurfaces of Lorentzian cosymplectic manifolds and Lorentzian paracontact Sasakian manifolds are also studied.
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J. L. Cabrerizo et al. [5] studied slant submanifolds of Sasakian and K- contact manifolds. Semi-slant submanifolds were introduced as a generalized version of CR-submanifold. Cabrerizo et al. [4] obtained interesting results for the semi-slant submanifold of Sasakian manifolds. The purpose of the present paper is to study slant and semi-slant submanifolds of a T-manifold.
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