Lorentzian $\alpha$-Sasakian Manifold with $\mathbf{W}_{3}$-Curvature Tensor

Abhıjıt Mandal; Mustafa Yıldırım; Bappaditya Debnath; Ashoke Das

doi:10.36753/mathenot.1975242

Lorentzian $\alpha$-Sasakian Manifold with $\mathbf{W}_{3}$-Curvature Tensor

Abstract

In the present paper, we investigate Lorentzian $\alpha $-Sasakian manifolds equipped with a semi-symmetric non-metric (SSNM) connection. First, we establish the existence and uniqueness of the SSNM-connection and derive several fundamental curvature properties associated with this connection. We then study the behavior of the $W_{3}$-curvature tensor on such manifolds and obtain characterizations of $\xi $-$\overline{W}_{3}$ -flat, $\phi $-$\overline{W}_{3}$-flat, and $\phi $-$\overline{W}_{3}$ -semi-symmetric Lorentzian $\alpha $-Sasakian manifolds. It is shown that under suitable curvature conditions, namely $\phi $-$\overline{W}_{3}$ -flatness and $\overline{W}_{3}.\overline{R}=0$, the manifold becomes a generalized $\eta $-Einstein manifold. Furthermore, scalar curvature relations are obtained for manifolds satisfying $\xi $-$\overline{W}_{3}$ -flatness, $\overline{W}_{3}.\overline{S}=0,$ $\overline{S}.\overline{W} _{3}=0$, and $\phi $-$\overline{W}_{3}$-semi-symmetry. Finally, a non-trivial $3$-dimensional example of a Lorentzian $\alpha $-Sasakian manifold admitting an SSNM-connection is constructed to verify the theoretical results. Here, $\overline{W}_{3},\overline{R}$ and $\overline{S} $ denote the $W_{3}$-curvature tensor, Riemannian curvature tensor and Ricci curvature tensor with respect to the SSNM-connection.

Keywords

Lorentzian $\alpha $-Sasakian manifold, Semi-symmetric non-metric connection, $W_{3}$-curvature tensor

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Abhıjıt Mandal
0000-0002-3979-8916
India

Mustafa Yıldırım ^*
0000-0002-7885-1492
Türkiye

Bappaditya Debnath
0000-0003-3515-9495
India

Ashoke Das
0000-0002-6612-0182
India

Early Pub Date

October 26, 2026

Publication Date

-

Submission Date

June 20, 2026

Acceptance Date

September 10, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.36753/mathenot.1975242

IZ

https://izlik.org/JA93AM83ZF

APA

Mandal, A., Yıldırım, M., Debnath, B., & Das, A. (2026). Lorentzian $\alpha$-Sasakian Manifold with $\mathbf{W}_{3}$-Curvature Tensor. Mathematical Sciences and Applications E-Notes, Advanced Online Publication, 229-246. https://doi.org/10.36753/mathenot.1975242

AMA

1.Mandal A, Yıldırım M, Debnath B, Das A. Lorentzian $\alpha$-Sasakian Manifold with $\mathbf{W}_{3}$-Curvature Tensor. Math. Sci. Appl. E-Notes. 2026;(Advanced Online Publication):229-246. doi:10.36753/mathenot.1975242

Chicago

Mandal, Abhıjıt, Mustafa Yıldırım, Bappaditya Debnath, and Ashoke Das. 2026. “Lorentzian $\alpha$-Sasakian Manifold With $\mathbf{W}_{3}$-Curvature Tensor”. Mathematical Sciences and Applications E-Notes, no. Advanced Online Publication: 229-46. https://doi.org/10.36753/mathenot.1975242.

EndNote

Mandal A, Yıldırım M, Debnath B, Das A (October 1, 2026) Lorentzian $\alpha$-Sasakian Manifold with $\mathbf{W}_{3}$-Curvature Tensor. Mathematical Sciences and Applications E-Notes Advanced Online Publication 229–246.

IEEE

[1]A. Mandal, M. Yıldırım, B. Debnath, and A. Das, “Lorentzian $\alpha$-Sasakian Manifold with $\mathbf{W}_{3}$-Curvature Tensor”, Math. Sci. Appl. E-Notes, no. Advanced Online Publication, pp. 229–246, Oct. 2026, doi: 10.36753/mathenot.1975242.

ISNAD

Mandal, Abhıjıt - Yıldırım, Mustafa - Debnath, Bappaditya - Das, Ashoke. “Lorentzian $\alpha$-Sasakian Manifold With $\mathbf{W}_{3}$-Curvature Tensor”. Mathematical Sciences and Applications E-Notes. Advanced Online Publication (October 1, 2026): 229-246. https://doi.org/10.36753/mathenot.1975242.

JAMA

1.Mandal A, Yıldırım M, Debnath B, Das A. Lorentzian $\alpha$-Sasakian Manifold with $\mathbf{W}_{3}$-Curvature Tensor. Math. Sci. Appl. E-Notes. 2026;:229–246.

MLA

Mandal, Abhıjıt, et al. “Lorentzian $\alpha$-Sasakian Manifold With $\mathbf{W}_{3}$-Curvature Tensor”. Mathematical Sciences and Applications E-Notes, no. Advanced Online Publication, Oct. 2026, pp. 229-46, doi:10.36753/mathenot.1975242.

Vancouver

1.Abhıjıt Mandal, Mustafa Yıldırım, Bappaditya Debnath, Ashoke Das. Lorentzian $\alpha$-Sasakian Manifold with $\mathbf{W}_{3}$-Curvature Tensor. Math. Sci. Appl. E-Notes. 2026 Oct. 1;(Advanced Online Publication):229-46. doi:10.36753/mathenot.1975242

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