The study of CR-submanifolds of a Kaehler manifold was initiated by Bejancu [1]. Since then many papers have appeared on CR-submanifolds. The aim of the present paper is to study generalised CR-submanifolds of a LP-Sasakian manifolds.

In this paper, generalised CR -submanifolds of an ) , (   -trans-Sasakian manifolds with semi-symmetric non-moetric connection are studied. Moreover, integrability conditions of the distributions on generalised CR -submanifolds of an ) , (   -trans-Sasakian manifolds with semi-symmetric non-moetric connection and geometry of leaves with semi-symmetric non-metric connection have been discussed. 2000 Mathematical Subject Classification :53C21, 53C25, 53C05.

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Generalised CR-submanifolds of a LP-sasakian manifolds

Generalised CR -submanifolds of an (, ) -trans-Sasakian manifold with certain connection

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The differential geometry of CR submanifolds of a Kaehler manifold is studied. Theorems on parallel normal sections and on a special type of flatness of the normal connection on a CR submanifold are obtained. Also, the nonexistence of totally umbilical proper CR submanifolds in an elliptic or hyperbolic complex space is proven.

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methods

submanifolds of a Kaehler manifold. I

background

On Lorentzian Paracontact Manifolds

A Lorentzian para-Sasakian manifold M$(\varphi, \zeta, \eta, g)$ (abr. LPS-manifold) has been defined and studied in [9] and [10]. On the other hand, para-Sasakian (abr. PS)-manifolds are special semi-cosympletic manifolds (in the sense of [2]), that is, they are endowed with an almost cosympletic 2-form $\Omega$ such that $d^{2\eta}\Omega = \psi(d^\omega$ denotes the cohomological operator [6]), where the 3-form $\psi$ is the associated Lefebvre form of $\Omega$ ([8]). If $\eta$ is exact, $\psi$ is a $d^{2\eta}$-exact form, the manifold M is called an exact Ps-manifold. Clearly, any LPS-manifold is endowed with a semi-cosymplectic structure (abr. SC-structure).

$zeta$-null geodesic gradient vector fields on a lorentzian para-sasakian manifold

Recently Matsumoto (1) introduced the idea of Lorentzian para contact structure and studied its several properties. In the present paper we studied the integrability condition of the distribution on semi-invariant submanifolds of LP-Sasakian manifold. p p p

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Semi-Invariant Submanifolds of a Lorentzian Para-Sasakian Manifold

The object of the paper is to study a Sasakian manifold with quasi-conformal curvature tensor.

Generalised CR-submanifolds of a LP-sasakian manifolds

Citations

Generalised CR -submanifolds of an (, ) -trans-Sasakian manifold with certain connection

References

submanifolds of a Kaehler manifold. I

On Lorentzian Paracontact Manifolds

$zeta$-null geodesic gradient vector fields on a lorentzian para-sasakian manifold

Semi-Invariant Submanifolds of a Lorentzian Para-Sasakian Manifold

LP-sasakian manifolds with quasi-conformal curvature tensor

Related Papers (5)

CR submanifolds of Kaehlerian and Sasakian manifolds

Generalised CR -submanifolds of an (, ) -trans-Sasakian manifold with certain connection

Generic submanifolds of Sasakian manifolds

Some results on LP-Sasakian manifolds

Cr submanifolds of a sasakian manifold