Some results on almost paracontact paracomplex Riemannian manifolds

Nülifer Özdemir; Şirin Aktay; Mehmet Solgun; Nülifer Özdemir; Şirin Aktay; Mehmet Solgun

doi:10.3934/math.2025489

AIMS Mathematics

2025, Volume 10, Issue 5: 10764-10786. doi: 10.3934/math.2025489

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Research article

Some results on almost paracontact paracomplex Riemannian manifolds

1.
Department of Mathematics, Eskişehir Technical University, Eskişehir 26470, Turkey
2.
Department of Mathematics, Bilecik Seyh Edebali University, Bilecik, Turkey

Received: 24 January 2025 Revised: 25 April 2025 Accepted: 30 April 2025 Published: 12 May 2025
MSC : 53C15, 53C25

In this study, a class of Riemannian almost product manifolds is obtained by the warped product of almost paracontact paracomplex Riemannian manifolds with $ \mathbb{R} $. The curvature properties of the almost product manifolds are studied. Then, normal almost paracontact paracomplex Riemannian manifolds are considered. It is proven that the almost paracontact paracomplex Riemannian manifolds are normal if and only if the almost product manifolds obtained by the warped product are integrable. In addition, examples of almost paracont paracomplex Riemannian manifolds are given.
- almost paracontact paracomplex Riemannian manifold,
- Riemannian almost product manifold,
- Einstein manifold,
- warped product
Citation: Nülifer Özdemir, Şirin Aktay, Mehmet Solgun. Some results on almost paracontact paracomplex Riemannian manifolds[J]. AIMS Mathematics, 2025, 10(5): 10764-10786. doi: 10.3934/math.2025489

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Abstract

In this study, a class of Riemannian almost product manifolds is obtained by the warped product of almost paracontact paracomplex Riemannian manifolds with $ \mathbb{R} $. The curvature properties of the almost product manifolds are studied. Then, normal almost paracontact paracomplex Riemannian manifolds are considered. It is proven that the almost paracontact paracomplex Riemannian manifolds are normal if and only if the almost product manifolds obtained by the warped product are integrable. In addition, examples of almost paracont paracomplex Riemannian manifolds are given.

References

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