In the present note we have introduced a new concept called generalized η-Einstein manifold in a 3-dimensional trans-Sasakian manifold and have given some preliminary ideas about the same. Inthe next section some geometric properties about this manifold have been deduced. Finally we havejustified the existence of such a manifold by citing an example.
Advanced Trends in Mathematics (Volume 2)
B. Laha "Generalized η-Einstein 3-Dimensional Trans-Sasakian Manifold", Advanced Trends in Mathematics, Vol. 2, pp. 28-32, 2015