On Semi-Invariant Submanifolds of Trans-Sasakian Finsler Manifolds

Abstract

We define trans-Sasakian Finsler manifold $\bar{F}^{2n+1}=(\mathcal{\bar{N}}, \mathcal{\bar{N^{\prime }}}, \bar{F})$ and semi-invariant submanifold $F^{m}=(\mathcal{N}, \mathcal {N^{\prime }}, F)$ of a trans-Sasakian Finsler manifold $\bar{F}^{2n+1}$. Then we study mixed totally geodesic and totally umbilical semi-invariant submanifolds of trans Sasakian Finsler manifold.