A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor

İnan Ünal; Mustafa Altın; Shashıkant Pandey

doi:10.47000/tjmcs.1632911

A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor

Abstract

In this study, we consider various geometric conditions associated with the vanishing of a generalized curvature tensor, namely the $\mathcal{T}$-tensor, on $N(\kappa)$-contact metric manifolds. We define and analyze several types of $\mathcal{T}$-flatness conditions, including $\mathcal{T}$-flat, $\xi$-$\mathcal{T}$-flat, quasi-$\mathcal{T}$-flat, and $\varphi$-$\mathcal{T}$-flat structures. By applying these flatness conditions, we obtain algebraic constraints on the curvature parameters, particularly involving the Ricci tensor. The resulting characterizations allow for the classification of $N(\kappa)$-contact metric manifolds as either Einstein or $\eta$-Einstein, depending on the specific values of the structure constants. These investigations also lead to deeper insights into the geometric structure and local isometry types of the manifolds under study.

Keywords

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

İnan Ünal ^*
0000-0003-1318-9685
Türkiye

Mustafa Altın
0000-0001-5544-5910
Türkiye

Shashıkant Pandey
0000-0002-8128-2884
India

Publication Date

December 30, 2025

Submission Date

February 4, 2025

Acceptance Date

July 11, 2025

Published in Issue

Year 2025 Volume: 17 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1632911

IZ

https://izlik.org/JA32GZ74SS

Cite

RIS / Bibtex

APA

Ünal, İ., Altın, M., & Pandey, S. (2025). A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor. Turkish Journal of Mathematics and Computer Science, 17(2), 550-561. https://doi.org/10.47000/tjmcs.1632911

AMA

1.Ünal İ, Altın M, Pandey S. A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor. TJMCS. 2025;17(2):550-561. doi:10.47000/tjmcs.1632911

Chicago

Ünal, İnan, Mustafa Altın, and Shashıkant Pandey. 2025. “A Classification of $ N(\kappa)$-Contact Metric Manifolds With $ \mathcal{T} $-Curvature Tensor”. Turkish Journal of Mathematics and Computer Science 17 (2): 550-61. https://doi.org/10.47000/tjmcs.1632911.

EndNote

Ünal İ, Altın M, Pandey S (December 1, 2025) A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor. Turkish Journal of Mathematics and Computer Science 17 2 550–561.

IEEE

[1]İ. Ünal, M. Altın, and S. Pandey, “A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor”, TJMCS, vol. 17, no. 2, pp. 550–561, Dec. 2025, doi: 10.47000/tjmcs.1632911.

ISNAD

Ünal, İnan - Altın, Mustafa - Pandey, Shashıkant. “A Classification of $ N(\kappa)$-Contact Metric Manifolds With $ \mathcal{T} $-Curvature Tensor”. Turkish Journal of Mathematics and Computer Science 17/2 (December 1, 2025): 550-561. https://doi.org/10.47000/tjmcs.1632911.

JAMA

1.Ünal İ, Altın M, Pandey S. A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor. TJMCS. 2025;17:550–561.

MLA

Ünal, İnan, et al. “A Classification of $ N(\kappa)$-Contact Metric Manifolds With $ \mathcal{T} $-Curvature Tensor”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 2, Dec. 2025, pp. 550-61, doi:10.47000/tjmcs.1632911.

Vancouver

1.İnan Ünal, Mustafa Altın, Shashıkant Pandey. A Classification of $ N(\kappa)$-contact Metric Manifolds with $ \mathcal{T} $-curvature Tensor. TJMCS. 2025 Dec. 1;17(2):550-61. doi:10.47000/tjmcs.1632911