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.

Keywords

• Trans-Sasakian Finsler manifold,Semi-invariant submanifold,Totally geodesic,Totally umbilical

References

1. [1] J. A. Oubina, New class of almost contact metric structures, Publ Math Debrecen, 32 (1958), 187–193.
2. [2] C. Gherge, Harmonicity on nearly trans-Sasaki manifolds, Demostratio Math., 33 (2000), 151–157.
3. [3] M. Kobayashi, Semi-invariant submanifolds of a certain class of almost contact manifolds, Tensor, 43 (1986), 28–36.
4. [4] S. J. Kim, X. Lin, M. M. Tripathi, On semi-invariant submanifolds of nearly trans-Sasakian manifolds, Int. J. Pure Appl. Math., (2004), 15–34.
5. [5] M. Ahmad, Semi-invariant submanifolds of nearly Kenmotsu manifoldwith the canonical semi-symmetric semi-metric connection, Mat. Vesnik, 62 (2009), 189–198.
6. [6] M. H. Shahid, Almost semi invariant submanifold of trans-Sasakian manifolds, Bull. Math. Soc. Sci. Math., Roumanie, 37(85) (3-4) (1993), 133–147.
7. [7] M. H. Shahid, F. R. Al-Solamy, J.B. Jun, M. Ahmad, Submersion of semi-invariant submanifolds of trans-Sasakian manifold, Bull. Malays. Math. Sci. Soc., 36(1) (2013)(2), 63—71.
8. [8] B. B. Sinha, R. K. Yadav, On almost trans-Sasakian Finsler manifolds, Indian J. Pure Appl. Math., 22(3) (1991), 185–192.

9. [9] A. F. Yaliniz, N. Caliskan, Sasakian Finsler manifolds, Turkish J. Math., 37(2) (2013), 319–339.