Some Solitons on Anti-Invariant Submanifolds of Para-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection

Mandal, Abhijit; Yıldırım, Mustafa; Al-Qashbari, Adel Mohammed Ali; Khan, Mohammad Nazrul Islam

doi:10.3390/sym18010030

Open AccessArticle

Some Solitons on Anti-Invariant Submanifolds of Para-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection

by

Abhijit Mandal

¹

,

Mustafa Yıldırım

²

,

Adel Mohammed Ali Al-Qashbari

³

and

Mohammad Nazrul Islam Khan

^4,*

¹

Department of Mathematics, Raiganj Surendranath Mahavidyalaya, Raiganj 733134, West Bengal, India

²

Department of Mathematics, Faculty of Science and Art, Aksaray University, 68100 Aksaray, Türkiye

³

Department of Med. Engineering, Faculty of Engineering and Computers, University of Science and Technology, Aden 124, Yemen

⁴

Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia

^*

Author to whom correspondence should be addressed.

Symmetry 2026, 18(1), 30; https://doi.org/10.3390/sym18010030

Submission received: 13 November 2025 / Revised: 9 December 2025 / Accepted: 18 December 2025 / Published: 23 December 2025

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 4th Edition)

Download Versions Notes

Abstract

The objective of this study is to investigate

ρ

-Einstein solitons on submanifolds of a para-Sasakian manifold under certain curvature conditions. The novelty of this work lies in the characterization of

ρ

-Einstein solitons on anti-invariant submanifolds of a para-Sasakian manifold equipped with a semi-symmetric non-metric connection, where the structure vector field is taken as the potential vector field. We establish several significant results concerning the classification of

ρ

-Einstein solitons with respect to the

W_{3}

-curvature tensor and the semi-symmetric non-metric connection. Moreover, we construct a non-trivial example of an anti-invariant submanifold of a five-dimensional para-Sasakian manifold by solving an associated system of partial differential equations.

Keywords: para-Sasakian manifold; semi-symmetric non-metric connection; ρ-Einstein soliton; mathematical operators; partial differential equations; W₃-curvature tensor

Share and Cite

MDPI and ACS Style

Mandal, A.; Yıldırım, M.; Al-Qashbari, A.M.A.; Khan, M.N.I. Some Solitons on Anti-Invariant Submanifolds of Para-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection. Symmetry 2026, 18, 30. https://doi.org/10.3390/sym18010030

AMA Style

Mandal A, Yıldırım M, Al-Qashbari AMA, Khan MNI. Some Solitons on Anti-Invariant Submanifolds of Para-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection. Symmetry. 2026; 18(1):30. https://doi.org/10.3390/sym18010030

Chicago/Turabian Style

Mandal, Abhijit, Mustafa Yıldırım, Adel Mohammed Ali Al-Qashbari, and Mohammad Nazrul Islam Khan. 2026. "Some Solitons on Anti-Invariant Submanifolds of Para-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection" Symmetry 18, no. 1: 30. https://doi.org/10.3390/sym18010030

APA Style

Mandal, A., Yıldırım, M., Al-Qashbari, A. M. A., & Khan, M. N. I. (2026). Some Solitons on Anti-Invariant Submanifolds of Para-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection. Symmetry, 18(1), 30. https://doi.org/10.3390/sym18010030

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Some Solitons on Anti-Invariant Submanifolds of Para-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI