Classification of Three-Dimensional Contact Metric Manifolds with Almost-Generalized Ƶ -Solitons

Shahroud Azami (), Mehdi Jafari and Daniele Ettore Otera ()
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Shahroud Azami: Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
Mehdi Jafari: Department of Mathematics, Payame Noor University, Tehran, Iran
Daniele Ettore Otera: Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University, LT-08412 Vilnius, Lithuania

Mathematics, 2025, vol. 13, issue 23, 1-12

Abstract: This work investigates the classification of three-dimensional complete contact metric manifolds that are non-Sasakian and satisfy the relation Q ξ = σ ξ , focusing on those that support an almost-generalized Ƶ -soliton. In the scenario where σ is constant, we prove that if a generalized Ƶ -soliton ( M n , g , δ , η , V , μ , Λ ) satisfies the condition g ( V , ξ ) = 0 , then M n must be either an Einstein manifold or locally isometric to the Lie group E ( 1 , 1 ) . Comparable classifications are obtained for ( κ , μ , ϑ ) -contact metric manifolds. Furthermore, we explore situations in which the potential vector field aligns with the Reeb vector field. We then provide the corresponding structural characterizations.

Keywords: generalized Ƶ -solitons; Sasakian manifold; Lie group; contact metric structure; isometry (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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