Semiparallel Submanifolds of a Normal Paracontact Metric Manifold

Abstract

The object of the present paper is to study invariant semiparallel and 2-semiparallel submanifolds of a normal paracontact metric manifold. We see that parallel submanifolds of a normal paracontact metric manifold are totally geodesic.

Keywords

• Riemannian curvature tensor,concircular curvature tensor,invariant submanifold,semiparallel and 2-semiparallel submanifolds

References

1. K. Arslan, U. Lumiste, C. Murathan and C. Özgür, 2-semiparallel surfaces in space forms 1. Two particular cases, Proc. Estonian Acad. Sci. Phys. Math. 49 (3), 139-148, 2000.
2. M. Atçeken and S. Uddin, Semi-invariant submanifolds of a normal Paracontact Man- ifold, Filomat, 31 (15), 4875-4887, 2017, doi.org/10.2298/FIL17155875A.
3. C.I. Bejan, Almost Semi-Invariant submanifolds of a cosymplectic manifold, An. Ştint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 31, 149-156, 1985.
4. A. Bejancu and N. Papaghuic, Semi-Invariant Submanifolds of a Sasakian manifold, An. Ştint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 27, 163-170, 1981.
5. A. Bejancu and N. Papaghuic, Semi-Invariant Submanifolds of a Sasakian space form, Collog. Math. 48, 77-88, 1984.
6. A. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosympectic man- ifold, Demonstratio Math. 19, 395-401, 1986.
7. I. Ishıhara, Anti-invariant submanifolds of a Sasakian space form, Kodai Math. J. 2, 171-186, 1979.
8. M.A. Khan, S. Uddin and R.Sachdeva, Semi-Invariant warped product submanifolds of cosymplectic manifolds, J. Inequal. Appl. 2012 (19), 2012, doi: 10. 1186/1029- 242X-2012-19.

9. J.S. Kim, X. Liu and M.M. Tripathi, On semi-invariant submanifolds of nearly trans- Sasakian manifolds, Int. J. Pure and Appl. Math. Sci. 1, 15-34, 2004.
10. M. Kon, Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep. 25, 330-336, 1973.
11. C. Özgür, F. Gürler and C. Murathan, On semiparallel anti invariant submanifolds of generalized Sasakian space forms, Turk J. Math. 38, 796-802, 2014.
12. M.H. Shahid, Anti-invariant submanifolds of a Kenmotsu manifold, Kuwait J. Sci. Eng. 23 (2), 1996.
13. A.A. Shaikh, Y. Matsuyama and S.K. Hui, On invariant submanifolds of $(LCS)_n$−manifolds, J. Egyptian Math. Soc. 24, 263-269, 2016.
14. S. Uddin, V.A. Khan and C. Özel, Classification of totally umbilical $\xi^{\perp}$ $CR$- submanifolds of cosymplectic manifolds, Rocky Mountain J. Math. 45 (1), 361-369, 2015.
15. S. Uddin and C. Özel, A classification theorem on totally umbilical submanifolds in a cosymplectic manifold, Hacet. J. Math. Stat. 43 (4), 635-640, 2014.
16. K. Yano and M. Kon, Anti-invariant submanifolds of a Sasakian space form, Tohoku Math. J. 29, 9-23, 1977.