2020Journal of PolytechnicOpen access

A Note on Nearly Hyperbolic Cosymplectic Manifolds

Müge Karadağ

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Submanifold, Integrable system, Manifold (fluid mechanics), Geodesic, Mathematics, Pure mathematics, Hyperbolic manifold, Mathematical analysis

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