Resumen de A remark on trans-Sasakian 3-manifolds

Yaning Wang, Wenjie Wang

• 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.