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1 – 2 of 2Mohan Khatri and Jay Prakash Singh
This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.
Abstract
Purpose
This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.
Design/methodology/approach
The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example.
Findings
We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S2n+1 and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to En+1 × Sn(4) in higher dimension.
Originality/value
All results are novel and generalizations of previously obtained results.
Details
Keywords
Mohd Danish Siddiqi, Sudhakar Kumar Chaubey and Aliya Naaz Siddiqui
The central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance…
Abstract
Purpose
The central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α-Sasakian manifold, Lorentzian β-Kenmotsu manifold and Lorentzian cosymplectic manifold. Furthermore, the authors discuss some results about Clairaut Lagrangian submersions whose total space is a Lorentzian trans-Sasakian manifolds of type (α, β). Finally, the authors furnished some examples based on this study.
Design/methodology/approach
This research discourse based on classifications of submersion, mainly Clairaut submersions, whose total manifolds is Lorentzian trans-Sasakian manifolds and its all classes like Lorentzian Sasakian, Lorenztian Kenmotsu and Lorentzian cosymplectic manifolds. In addition, the authors have explored some axioms of Clairaut Lorentzian submersions and illustrates our findings with some non-trivial examples.
Findings
The major finding of this study is to exhibit a necessary and sufficient condition for a submersions to be a Clairaut submersions and also find a condition for Clairaut Lagrangian submersions from Lorentzian trans-Sasakian manifolds.
Originality/value
The results and examples of the present manuscript are original. In addition, more general results with fair value and supportive examples are provided.
Details