Integrability Conditions Of Distributions Research Articles

Screen almost semi-invariant lightlike submanifolds of indefinite Kaehler manifolds

In this paper, we introduce screen almost semi-invariant (SASI)-lightlike submanifolds of indefinite Kaehler manifolds. We obtain the necessary and sufficient condition for the induced connection to be a metric connection on SASI-lightlike submanifolds and construct an example for this manifold. Also, we find some conditions for integrability of distributions and investigate certain characterizations.

Half Lightlike Submanifolds of A Golden Semi-Riemannian Manifold

We present half lightlike submanifolds of a golden semi-Riemannian manifold. We prove that there is no radical anti-invariant half lightlike submanifold of a golden semi-Riemannian manifold. We get results for screen semi-invariant half lightlike submanifolds of a golden semi-Riemannian manifold. We prove the conditions for integrability of distributions on screen semi-invariant half lightlike submanifolds and investigate the geometry of leaves of distributions. Moreover, we study screen conformal half lightlike submanifolds of a golden semi-Riemannian manifold.

A Note on Nearly Hyperbolic Cosymplectic Manifolds

Interest in hyperbolic cosymplectic manifolds has increased in recent years. In this paper, pseudo slant submanifolds of a nearly hyperbolic cosymplectic manifold have been explored deeply. In particular, the integrability conditions of distributions on such manifolds have been investigated. So, for a pseudo submanifold M of a nearly hyperbolic cosymplectic manifold M ̃ which is totally geodesic, D_θ,D_( _μ ) distributions with〖 D〗_( _μ )⊕⟨ξ⟩ and D_θ⊕D_( _μ ) are proved integrable but D_( _θ )⊕⟨ξ⟩ or not.

Quasi hemi-slant submanifolds of cosymplectic manifolds

We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate the necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.

Quasi hemi-slant submanifolds of Sasakian manifolds

In this paper, we define and study quasi hemi-slant submanifolds as a generalization of slant submanifolds, semi-slant submanifolds and hemi-slant submanifolds of contact metric manifolds [ In particular, for a Sasakian manifold]. Further, we obtain necessary and sufficient conditions for integrability of distributions which are involved in the definition of quasi hemi-slant submanifolds of Sasakian manifolds. After it, we investigate the necessary and sufficient condition for quasi hemi-slant submanifolds of Sasakian manifolds to be totally geodesic. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product Riemannian manifold and also give an example of such submanifolds.

Altın semi-Riemann manifoldların semi-invaryant lightlike altmanifoldları

In this study, we introduce semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. We find some conditions for integrability of distributions. Morever, we investigate totally geodesic and mixed geodesic distributions of such a submanifold. The paper also contains an example.

Some Result on Contact Pseudo-Slant Submanifolds of a Sasakian Manifold

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a Sasakian manifold. We derive the integrability conditions of distributions in the definition of a contact pseudo-slant submanifold. The notions contact pseudo-slant product is defined, and the necessary and sufficient conditions for a submanifold to contact pseudo-slant product is given. Also, a non-trivial example is used to demonstrate that the method presented in this paper is effective.

Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection

We study lightlike submanifolds of a semi-Riemannian product manifold. We introduce a class of lightlike submanifolds called screen semi-invariant lightlike submanifold. We consider lightlike submanifolds with respect to a quarter symmetric non-metric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.

Radical transversal screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds

In this paper, we introduce the notion of radical transversal screen semi-slant lightlike submanifolds of indefinite Sasakianmanifolds giving some non-trivial examples and give characterization theorem of such submanifolds. Integrability conditions of distributions D 1, D 2 and RadTM on radical transversal screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds have been obtained. Further we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic. We also study mixed geodesic radical transversal screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds.

Radical Transversal Lightlike Submanifolds of Indefinite Para-Sasakian Manifolds

Abstract 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.

Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter-Symmetric Nonmetric Connections

We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical anti-invariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quarter-symmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.