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Trans-Sasakian manifolds homothetic to Sasakian manifolds
CHAND U DE
Published in Kossuth Lajos Tudomanyegyetem
2016
Volume: 88

Issue: 43528
Pages: 439 - 448
Abstract
In this paper, we obtain necessary and sufficient conditions for a 3-dimensional compact and connected trans-Sasakian manifold of type (α, β) to be homothetic to a Sasakian manifold. We also show that if a compact trans-Sasakian manifold admits an isometric immersion in the Euclidean space R4 with Reeb vector field being transformation of unit normal vector field under the complex structure of R4, then it is homothetic to a Sasakian manifold. We also introduce the axiom of flat torus for a 3-dimensional trans-Sasakian manifold and show that a 3-dimensional connected trans-Sasakian manifold with Ricci curvature in the direction of Reeb vector field a nonzero constant, satisfying axiom of flat torus is homothetic to a Sasakian manifold.