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Kazemi M B, Salahvarzi S. Statistical cosymplectic manifolds and their submanifolds. mmr 2022; 8 (2) :203-215

URL: http://mmr.khu.ac.ir/article-1-2783-en.html

URL: http://mmr.khu.ac.ir/article-1-2783-en.html

Let

On the other hand, one of the most important structures on odd dimensional Riemannian manifolds is the almost contact structure. Recently, statistical manifolds equipped with almost contact structures are studied by many authors. In this paper, we introduce statistical almost contact-like and statistical cosymplectic manifolds on a Riemannian manifold. We recall the basic definitions and define statistical cosymplectic manifolds and their invariant submanifolds. We prove that an invariant submanifold of a statistical cosymplectic manifold with tangent structure vector field is a cosymplectic and minimal-like submanifold. Also, we prove if the structure vector field be normal to the submanifold then the submanifold is a statistical Keahler-like manifold. Finally, we construct two examples to illustrate some results of the paper.

Let

Moreover, an affine and torsion free connection

An almost contact manifold

Let

We show that the manifold

We introduce statistical cosymplectic manifolds and investigate some properties of their tensors. We define invariant and anti-invariant submanifolds and study invariant submanifolds with normal and tangent structure vector fields. We prove that an invariant submanifold of a statistical cosymplectic manifold with tangent structure vector field is a cosymplectic and minimal-like submanifold. Also we show if the structure vector field is normal to the submanifold then that is a statistical Keahler-like manifold

Type of Study: S |
Subject:
Differential Geometry

Received: 2018/05/22 | Revised: 2022/11/16 | Accepted: 2020/08/5 | Published: 2022/05/21 | ePublished: 2022/05/21

Received: 2018/05/22 | Revised: 2022/11/16 | Accepted: 2020/08/5 | Published: 2022/05/21 | ePublished: 2022/05/21

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