On a Class of Three-Dimensional Trans-Sasakian Manifolds

A note on trans-Sasakian manifolds

“…Since then, there is a concentration on studying geometry of 3-dimensional trans-Sasakian manifolds only (cf. [1], [4], [5], [9], [10]), putting some restrictions on the smooth functions α, β appearing in the definition of trans-Sasakian manifolds. There are several examples of trans-Sasakian manifolds constructed mostly on 3-dimensional Riemannian manifolds (cf.…”

On invariant submanifolds of trans-Sasakian manifolds

“…Also, in this section an interesting corollary and an important remark concerning submanifolds of α-Sasakian and β -Kenmotsu manifolds are added. In this connection we mention that recently trans-Sasakian manifolds and their submanifolds were studied in [8,9].…”

Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator

“…Under what condition is a trans-Sasakian 3-manifold proper? De [7][8][9][10][11][12], Deshmukh [13][14][15], Wang and Liu [16] and Wang [2,17] answered this question from various points of view. In this paper, we study this question under a new geometric condition.…”