Schur-type inequality for solitonic hypersurfaces in $ (k, \mu) $-contact metric manifolds

Mohd Danish Siddiqi; Fatemah Mofarreh; Mohd Danish Siddiqi; Fatemah Mofarreh

doi:10.3934/math.20241711

AIMS Mathematics

2024, Volume 9, Issue 12: 36069-36081. doi: 10.3934/math.20241711

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Research article

Schur-type inequality for solitonic hypersurfaces in $ (k, \mu) $-contact metric manifolds

Mohd Danish Siddiqi ^{1
,
,},
Fatemah Mofarreh ^{2
,
,}

1.
Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 45142, Saudi Arabia
2.
Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia

Received: 20 September 2024 Revised: 15 December 2024 Accepted: 19 December 2024 Published: 26 December 2024
MSC : 53B30, 53C44, 53C50, 53C80

In this article, we derive a Schur-type Inequality in terms of the gradient $ r $-Almost Newton-Ricci-Yamabe soliton in $ (k, \mu) $-contact metric manifolds. We discuss the triviality for the compact gradient $ r $-Almost Newton-Ricci-Yamabe soliton in $ (k, \mu) $-Contact metric manifolds. In the end, we deduce a Schur-type inequality for the gradient $ r $-Almost Newton-Yamabe soliton in $ (k, \mu) $-contact metric manifolds, static Riemannian manifolds, and normal homogeneous compact Riemannian manifolds coupled with a projected Casimir operator.
- $ (k, \mu) $-contact metric manifold,
- Schur-type inequality,
- hypersurfaces,
- gradient $ r $-almost Newton-Ricci-Yamabe solitons
Citation: Mohd Danish Siddiqi, Fatemah Mofarreh. Schur-type inequality for solitonic hypersurfaces in $ (k, \mu) $-contact metric manifolds[J]. AIMS Mathematics, 2024, 9(12): 36069-36081. doi: 10.3934/math.20241711

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Abstract

In this article, we derive a Schur-type Inequality in terms of the gradient $ r $-Almost Newton-Ricci-Yamabe soliton in $ (k, \mu) $-contact metric manifolds. We discuss the triviality for the compact gradient $ r $-Almost Newton-Ricci-Yamabe soliton in $ (k, \mu) $-Contact metric manifolds. In the end, we deduce a Schur-type inequality for the gradient $ r $-Almost Newton-Yamabe soliton in $ (k, \mu) $-contact metric manifolds, static Riemannian manifolds, and normal homogeneous compact Riemannian manifolds coupled with a projected Casimir operator.

References

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