Metallic deformation on para-Sasaki-like para-Norden manifold

Rabia Cakan Akpınar; Esen Kemer Kansu; Rabia Cakan Akpınar; Esen Kemer Kansu

doi:10.3934/math.2024932

AIMS Mathematics

2024, Volume 9, Issue 7: 19125-19136. doi: 10.3934/math.2024932

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Metallic deformation on para-Sasaki-like para-Norden manifold

Department of Mathematics, Kafkas University, Kars 36100, Turkey

Received: 20 March 2024 Revised: 13 May 2024 Accepted: 22 May 2024 Published: 07 June 2024
MSC : 53C15, 53C25, 53C50

The main goal of this paper is to define the concept of metallic deformation through a relation between the metallic structure and paracontact structure on an almost paracontact para-Norden manifold. A Riemannian connection is obtained on a metallically deformed para-Sasaki-like para-Norden manifold. A $ \varphi $-connection is obtained via the Riemannian connection on a metallically deformed para-Sasaki-like para-Norden manifold. The curvature tensors, Ricci tensors, scalar curvatures, and $ \ast $-scalar curvatures are investigated with respect to the Riemannian connection and the $ \varphi $-connection. Finally, an example is given of a metallically deformed $ 3 $-dimensional para-Sasaki-like para-Norden manifold.
- para-Sasaki-like para-Norden manifold,
- paracontact structure,
- metallic deformation
Citation: Rabia Cakan Akpınar, Esen Kemer Kansu. Metallic deformation on para-Sasaki-like para-Norden manifold[J]. AIMS Mathematics, 2024, 9(7): 19125-19136. doi: 10.3934/math.2024932

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Abstract

The main goal of this paper is to define the concept of metallic deformation through a relation between the metallic structure and paracontact structure on an almost paracontact para-Norden manifold. A Riemannian connection is obtained on a metallically deformed para-Sasaki-like para-Norden manifold. A $ \varphi $-connection is obtained via the Riemannian connection on a metallically deformed para-Sasaki-like para-Norden manifold. The curvature tensors, Ricci tensors, scalar curvatures, and $ \ast $-scalar curvatures are investigated with respect to the Riemannian connection and the $ \varphi $-connection. Finally, an example is given of a metallically deformed $ 3 $-dimensional para-Sasaki-like para-Norden manifold.

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