Interaction of Codazzi Pairs with Almost Para Norden Manifolds

Sibel TURANLI; Sedanur UÇAN

doi:https://doi.org/10.47000/tjmcs.1075806

Makale detayları

Interaction of Codazzi Pairs with Almost Para Norden Manifolds

Yazarlar:

Sibel TURANLI | Sedanur UÇAN

Yayıncı:

Matematikçiler Derneği

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics and Computer Science 2022 Vol.14 Issue 1, pp.212-227

Belge Tipi:

Makale

Yayın Tarihi:

6/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000638359

Sıklık:

İki Yıllık

eISSN:

2148-1830

DOI:

https://doi.org/10.47000/tjmcs.1075806

Özet:

 

In this paper, we research some properties of Codazzi pairs on almost para Norden manifolds. Let (M2n, φ, g,G)(M2n, φ, g,G)(M_{2n},\ \varphi ,\ g,G) be an almost para Norden manifold. Firstly, ggg-conjugate connection, GGG-conjugate connection and φφ\varphi -conjugate connection of a linear connection ∇∇\mathrm{\nabla } on M2nM2nM_{2n} denoted by ∇∗ , ∇† ∇∗ , ∇† {\mathrm{\nabla }}^{*\
},\ {\mathrm{\nabla }}^{\dagger \ } and ∇φ ∇φ {\mathrm{\nabla }}^{\varphi \ } are defined and it is demonstrated that on the spaces of linear connections, (id, ∗,†,φ)(id, ∗,†,φ)\left(id,\ *,\dagger ,\varphi \right) acts as the four-element Klein group. We also searched some properties of these three types conjugate
connections. Then, Codazzi pairs (∇,φ) ,(∇,g)(∇,φ) ,(∇,g)\left(\mathrm{\nabla },\varphi \right)\ ,\left(\mathrm{\nabla },g\right) and (∇,G)(∇,G)\left(\mathrm{\nabla },G\right) are introduced and some properties of them are given. Let R , R∗ R , R∗ R\ ,\ R^{*\ }and R† R† R^{\dagger \ }are (0,4)(0,4)(0,4)-curvature tensors of conjugate connections
 ∇ , ∇∗ ∇ , ∇∗ \mathrm{\nabla }\mathrm{\ ,\ }{\mathrm{\nabla }}^{*\ }and ∇† ∇† {\mathrm{\nabla }}^{\dagger \ }, respectively. The relationship among the curvature tensors is investigated. The condition of Nφ=0Nφ=0N_{\varphi }=0 is obtained, where NφNφN_{\varphi } is Nijenhuis tensor field on M2nM2nM_{2n} and it is known
that the condition of integrability of almost para complex structure φφ\varphi  is Nφ=0Nφ=0N_{\varphi }=0. In addition, Tachibana operator is applied to the pure metric ggg and a necessary and sufficient condition (M,φ, g,G)(M,φ, g,G)\left(M,\varphi ,\ g,G\right) being a para Kahler Norden manifold is found. Finally, we examine φφ\varphi -invariant linear connections and statistical manifolds.

Makale detayları

Interaction of Codazzi Pairs with Almost Para Norden Manifolds

Yazarlar: Sibel TURANLI | Sedanur UÇAN

Yayıncı: Matematikçiler Derneği

Ana Başlıklar: Matematik

Dergi: Turkish Journal of Mathematics and Computer Science 2022 Vol.14 Issue 1, pp.212-227

Belge Tipi: Makale

Yayın Tarihi: 6/2022

Belge Dili: İngilizce

Document ID (Org No.): 2000638359

Sıklık: İki Yıllık

eISSN: 2148-1830

DOI: https://doi.org/10.47000/tjmcs.1075806

Sayı

Yazarlar:

Sibel TURANLI | Sedanur UÇAN

Yayıncı:

Matematikçiler Derneği

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics and Computer Science 2022 Vol.14 Issue 1, pp.212-227

Belge Tipi:

Makale

Yayın Tarihi:

6/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000638359

Sıklık:

İki Yıllık

eISSN:

2148-1830

DOI:

https://doi.org/10.47000/tjmcs.1075806