A remark on trans-Sasakian 3-manifolds

Yaning Wang ^[1] ; Wenjie Wang ^[2]
1. [1] Henan Normal University
  
  Henan Normal University
  
  China
2. [2] Dalian University of Technology
  
  Dalian University of Technology
  
  China
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 1, 2019, págs. 257-264
Idioma: inglés
DOI: 10.33044/revuma.v60n1a16
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Resumen
- Let M be a trans-Sasakian 3-manifold of type (α,β). In this paper, we give a negative answer to the question proposed by S. Deshmukh [Mediterr. J. Math. 13 (2016), no. 5, 2951–2958], namely we prove that the differential equation ∇β=ξ(β)ξ on M does not necessarily imply that M is homothetic to either a Sasakian or osymplectic manifold even when M is compact. Many examples are constructed to illustrate this result.