Certain results on tangent bundle endowed with generalized Tanaka Webster connection (GTWC) on Kenmotsu manifolds

Rajesh Kumar; Sameh Shenawy; Lalnunenga Colney; Nasser Bin Turki; Rajesh Kumar; Sameh Shenawy; Lalnunenga Colney; Nasser Bin Turki

doi:10.3934/math.20241465

AIMS Mathematics

2024, Volume 9, Issue 11: 30364-30383. doi: 10.3934/math.20241465

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Research article

Certain results on tangent bundle endowed with generalized Tanaka Webster connection (GTWC) on Kenmotsu manifolds

1.
Department of Mathematics, Pachhunga University College (Mizoram University), 796001, India
2.
Basic Science Department, Modern Academy for Engineering and Technology, Maadi, Egypt
3.
Department of Mathematics and Computer Science, Mizoram University, 796004, India
4.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 05 September 2024 Revised: 08 October 2024 Accepted: 14 October 2024 Published: 25 October 2024
MSC : 53C05, 53C25, 53D15, 53E20, 58A30

This work studies the complete lifts of Kenmotsu manifolds associated with the generalized Tanaka-Webster connection (GTWC) in the tangent bundle. Using the GTWC, this study explores the complete lifts of various curvature tensors and geometric structures from Kenmotsu manifolds to their tangent bundles. Specifically, it examines the complete lifts of Ricci semi-symmetry, the projective curvature tensor, $ \Phi $-projectively semi-symmetric structures, the conharmonic curvature tensor, the concircular curvature tensor, and the Weyl conformal curvature tensor. Additionally, the research delves into the complete lifts of Ricci solitons on Kenmotsu manifolds with the GTWC within the tangent bundle framework, providing new insights into their geometric properties and symmetries in the lifted space. The data on the complete lifts of the Ricci soliton in Kenmotsu manifolds associated with the GTWC in the tangent bundle are also investigated. An example of the complete lifts of a $ 5 $-dimensional Kenmotsu manifold is also included.
- Kenmotsu manifolds,
- generalized Tanaka-Webster connection,
- Einstein manifolds,
- curvature tensors,
- vertical and complete lifts,
- Ricci soliton,
- tangent bundle,
- partial differential equation,
- mathematical operators
Citation: Rajesh Kumar, Sameh Shenawy, Lalnunenga Colney, Nasser Bin Turki. Certain results on tangent bundle endowed with generalized Tanaka Webster connection (GTWC) on Kenmotsu manifolds[J]. AIMS Mathematics, 2024, 9(11): 30364-30383. doi: 10.3934/math.20241465

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Abstract

This work studies the complete lifts of Kenmotsu manifolds associated with the generalized Tanaka-Webster connection (GTWC) in the tangent bundle. Using the GTWC, this study explores the complete lifts of various curvature tensors and geometric structures from Kenmotsu manifolds to their tangent bundles. Specifically, it examines the complete lifts of Ricci semi-symmetry, the projective curvature tensor, $ \Phi $-projectively semi-symmetric structures, the conharmonic curvature tensor, the concircular curvature tensor, and the Weyl conformal curvature tensor. Additionally, the research delves into the complete lifts of Ricci solitons on Kenmotsu manifolds with the GTWC within the tangent bundle framework, providing new insights into their geometric properties and symmetries in the lifted space. The data on the complete lifts of the Ricci soliton in Kenmotsu manifolds associated with the GTWC in the tangent bundle are also investigated. An example of the complete lifts of a $ 5 $-dimensional Kenmotsu manifold is also included.

References

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