The purpose of this paper is to study pointwise bi-slant submanifolds of trans-Sasakian manifold. Firstly, we obtain a non-trivial example of a pointwise bi-slant submanifolds of an almost contact metric manifold. Next we provide some fundamental results, including a characterization for warped product pointwise bi-slant submanifolds in trans-Sasakian manifold. Then we establish that there does not exist warped product pointwise bi-slant submanifold of trans-Sasakian manifold \tilde{M} under some certain considerations. Next, we consider that M is a proper pointwise bi-slant submanifold of a trans-Sasakian manifold \tilde{M} with pointwise slant distrbutions \mathcal{D}_1\oplus<\xi> and \mathcal{D}_2, then using Hiepko’s Theorem, M becomes a locally warped product submanifold of the form M_1\times_fM_2, where M_1 and M_2 are pointwise slant submanifolds with the slant angles \theta_1 and \theta_2 respectively. Later, we show that pointwise bi-slant submanifolds of trans-Sasakian manifold become Einstein manifolds admitting Ricci soliton and gradient Ricci soliton under some certain conditions..




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Pahan, Sampa