Research Article
Year 2019,
Volume: 1 Issue: 2, 8 - 14, 09.10.2019
Abstract
The object of this paper is to study submanifolds of (k,¹)-paracontact
manifolds. We ¯nd the necessary and su±cient conditions for a submanifold of
(k,¹)-paracontact manifolds to be invariant and anti-invariant. Also, we research
the necessary and su±cient conditions for a submanifold of a (k,¹)-paracontact to be
semi-parallel and 2-semi-parallel submanifold and get interesting results.
References
- 1. K. Arslan, U. Lumiste, C. Murathan and C. Özgür, 2-semiparallel surfaces in space forms 1. Twoparticular cases, Proceedings of the Estonian Academy of Sciences, Physics and Mathematics 49,(3), 139-148, 2000.
- 2.M. Atceken, Yildirim U. and Dirik, S., Semiparallel Submanifolds of a Normal Paracontact MetricManifold. Hacettepe Journal of Mathematics and Statistics, 48(2), 501-509, 2019.
- 3. M. At»ceken and S. Uddin, Semi-invariant submanifolds of a normal Paracontact Manifold, Filomat,31(15), 4875-4887, 2017, doi.org/10.2298/FIL17155875A.
- 4. C. I. Bejan, Almost Semi-Invariant submanifolds of a cosymplectic manifold, An. S»tint. Univ. Al.I. Cuza Ia»si. Mat. (N.S. ) 31, 149-156, 1985.
- 5. Bejancu and N. Papaghuic, Semi-Invariant Submanifolds of a Sasakian manifold, An. S»tint.Univ. Al. I. Cuza Ia»si. Mat. (N. S) 27, 163-170, 1981.
- 6. Bejancu and N. Papaghuic, Semi-Invariant Submanifolds of a Sasakian space form, Collog.Math. 48, 77-88, 1984.
- 7. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosympectic manifold, Demon-stratio Math. 19, 395-401, 1986.
- 8. Ish³hara, Anti-invariant submanifolds of a Sasakian space form, Kodai Math. J. 2, 171-186,1979.
- 9. M. A. Khan, S. Uddin, and R.Sachdeva, Semi-Invariant warped product submanifolds of cosymplec-tic manifolds, Journal of Inequalities and Applications. doi: 10. 1186/1029-242X-2012-19, 2012.
- 10. M. Kon, Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep. 25,330-336, 1973.
- 11. S. Kim, X. Liu and M. M. Tripathi, On semi-invariant submanifolds of nearly trans-Sasakianmanifolds, Int. J. Pure and Appl. Math. Sci. 1, 15-34, 2004.
- 12. Özgür, F. Gürler and C. Murathan, On semiparallel anti invariant submanifolds of generalizedSasakian space forms, Turk J. Math. 38, 796-802, 2014.
- 13. M. H. Shahid, Anti-invariant submanifolds of a Kenmotsu manifold, Kuwait J. Sci. Eng. 23 (2),1996.
- 14. Shaikh, Y. Matsuyama and S.K. Hui, On invariant submanifolds of (LCS)n¡manifolds,Journal of the Egyptian Math. Soc., 24, 263-269, 2016.
- 15. S. Uddin and C. Ä Ozel, A classification theorem on totally umbilical submanifolds in a cosymplecticmanifold, Hacettepe Journal of Mathematics and Statistics, 43(4), 635-640, 2014.
- 16. S. Uddin, V.A. Khan and C. Ä Ozel, Classfication of totally umbilical »? CR-submanifolds of cosym-plectic manifolds, Rocky Mountain J. Math. 45(1), 361-369, 2015.
- 17. Yano and M. Kon, Anti-invariant submanifolds of a Sasakian space form, Tohoku Math. J. 29,9-23, 1977.
Year 2019,
Volume: 1 Issue: 2, 8 - 14, 09.10.2019
Abstract
Supporting Institution
17. geometri sempozyumu
References
- 1. K. Arslan, U. Lumiste, C. Murathan and C. Özgür, 2-semiparallel surfaces in space forms 1. Twoparticular cases, Proceedings of the Estonian Academy of Sciences, Physics and Mathematics 49,(3), 139-148, 2000.
- 2.M. Atceken, Yildirim U. and Dirik, S., Semiparallel Submanifolds of a Normal Paracontact MetricManifold. Hacettepe Journal of Mathematics and Statistics, 48(2), 501-509, 2019.
- 3. M. At»ceken and S. Uddin, Semi-invariant submanifolds of a normal Paracontact Manifold, Filomat,31(15), 4875-4887, 2017, doi.org/10.2298/FIL17155875A.
- 4. C. I. Bejan, Almost Semi-Invariant submanifolds of a cosymplectic manifold, An. S»tint. Univ. Al.I. Cuza Ia»si. Mat. (N.S. ) 31, 149-156, 1985.
- 5. Bejancu and N. Papaghuic, Semi-Invariant Submanifolds of a Sasakian manifold, An. S»tint.Univ. Al. I. Cuza Ia»si. Mat. (N. S) 27, 163-170, 1981.
- 6. Bejancu and N. Papaghuic, Semi-Invariant Submanifolds of a Sasakian space form, Collog.Math. 48, 77-88, 1984.
- 7. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosympectic manifold, Demon-stratio Math. 19, 395-401, 1986.
- 8. Ish³hara, Anti-invariant submanifolds of a Sasakian space form, Kodai Math. J. 2, 171-186,1979.
- 9. M. A. Khan, S. Uddin, and R.Sachdeva, Semi-Invariant warped product submanifolds of cosymplec-tic manifolds, Journal of Inequalities and Applications. doi: 10. 1186/1029-242X-2012-19, 2012.
- 10. M. Kon, Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep. 25,330-336, 1973.
- 11. S. Kim, X. Liu and M. M. Tripathi, On semi-invariant submanifolds of nearly trans-Sasakianmanifolds, Int. J. Pure and Appl. Math. Sci. 1, 15-34, 2004.
- 12. Özgür, F. Gürler and C. Murathan, On semiparallel anti invariant submanifolds of generalizedSasakian space forms, Turk J. Math. 38, 796-802, 2014.
- 13. M. H. Shahid, Anti-invariant submanifolds of a Kenmotsu manifold, Kuwait J. Sci. Eng. 23 (2),1996.
- 14. Shaikh, Y. Matsuyama and S.K. Hui, On invariant submanifolds of (LCS)n¡manifolds,Journal of the Egyptian Math. Soc., 24, 263-269, 2016.
- 15. S. Uddin and C. Ä Ozel, A classification theorem on totally umbilical submanifolds in a cosymplecticmanifold, Hacettepe Journal of Mathematics and Statistics, 43(4), 635-640, 2014.
- 16. S. Uddin, V.A. Khan and C. Ä Ozel, Classfication of totally umbilical »? CR-submanifolds of cosym-plectic manifolds, Rocky Mountain J. Math. 45(1), 361-369, 2015.
- 17. Yano and M. Kon, Anti-invariant submanifolds of a Sasakian space form, Tohoku Math. J. 29,9-23, 1977.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | October 9, 2019 |
| Published in Issue | Year 2019 Volume: 1 Issue: 2 |
