Geometric aspects of weakly symmetric and almost pseudo symmetric $ K $-contact manifolds admitting a non-symmetric non-metric connection

Rajesh Kumar; Laltluangkima Chawngthu; Oğuzhan Bahadır; Md Aquib; Rajesh Kumar; Laltluangkima Chawngthu; Oğuzhan Bahadır; Md Aquib

doi:10.3934/math.2025814

AIMS Mathematics

2025, Volume 10, Issue 8: 18232-18251. doi: 10.3934/math.2025814

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Research article

Geometric aspects of weakly symmetric and almost pseudo symmetric $ K $-contact manifolds admitting a non-symmetric non-metric connection

1.
Department of Mathematics, Pachhunga University College, Mizoram University, Aizawl-796001, Mizoram, India
2.
Department of Mathematics and Computer Science, Mizoram University, Tanhril, Aizawl-796004, Mizoram, India
3.
Department of Mathematics, Faculty of Sciences, Kahramanmaras Sutcu Imam University, Kahramanmaras 46100, Turkey
4.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box-65892, Riyadh 11566, Saudi Arabia

Received: 24 June 2025 Revised: 06 August 2025 Accepted: 08 August 2025 Published: 13 August 2025
MSC : 53C05, 53C15, 53C25, 53D10

In this paper, we explore the conditions for several geometric structures-specifically, weakly symmetric, weakly Ricci symmetric, almost pseudo symmetric, and almost pseudo Ricci symmetric–on a $ K $-contact manifold equipped with a non-symmetric non-metric connection. We present key theoretical results that characterize these structures in the context of such a connection. To illustrate the applicability of our findings, we construct an explicit example of a 3-dimensional $ K $-contact manifold with a non-symmetric non-metric connection. This example not only confirms the validity of the derived conditions but also offers a concrete model for further investigation in the field. Our results extend the understanding of geometric structures on $ K $-contact manifolds beyond the classical framework of the Levi-Civita connection, paving the way for new directions in differential geometry and mathematical physics.
- non-symmetric non-metric connection,
- Levi-Civita connection,
- curvature tensors,
- $ K $-contact manifold,
- weakly symmetric
Citation: Rajesh Kumar, Laltluangkima Chawngthu, Oğuzhan Bahadır, Md Aquib. Geometric aspects of weakly symmetric and almost pseudo symmetric $ K $-contact manifolds admitting a non-symmetric non-metric connection[J]. AIMS Mathematics, 2025, 10(8): 18232-18251. doi: 10.3934/math.2025814

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Abstract

In this paper, we explore the conditions for several geometric structures-specifically, weakly symmetric, weakly Ricci symmetric, almost pseudo symmetric, and almost pseudo Ricci symmetric–on a $ K $-contact manifold equipped with a non-symmetric non-metric connection. We present key theoretical results that characterize these structures in the context of such a connection. To illustrate the applicability of our findings, we construct an explicit example of a 3-dimensional $ K $-contact manifold with a non-symmetric non-metric connection. This example not only confirms the validity of the derived conditions but also offers a concrete model for further investigation in the field. Our results extend the understanding of geometric structures on $ K $-contact manifolds beyond the classical framework of the Levi-Civita connection, paving the way for new directions in differential geometry and mathematical physics.

References

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