Research Article
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Year 2019, Volume: 48 Issue: 2, 501 - 509, 01.04.2019

Abstract

References

  • 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.
  • 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.
  • 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.
  • 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.
  • A. Bejancu and N. Papaghuic, Semi-Invariant Submanifolds of a Sasakian space form, Collog. Math. 48, 77-88, 1984.
  • A. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosympectic man- ifold, Demonstratio Math. 19, 395-401, 1986.
  • I. Ishıhara, Anti-invariant submanifolds of a Sasakian space form, Kodai Math. J. 2, 171-186, 1979.
  • 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.
  • 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.
  • M. Kon, Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep. 25, 330-336, 1973.
  • C. Özgür, F. Gürler and C. Murathan, On semiparallel anti invariant submanifolds of generalized Sasakian space forms, Turk J. Math. 38, 796-802, 2014.
  • M.H. Shahid, Anti-invariant submanifolds of a Kenmotsu manifold, Kuwait J. Sci. Eng. 23 (2), 1996.
  • A.A. Shaikh, Y. Matsuyama and S.K. Hui, On invariant submanifolds of $(LCS)_n$−manifolds, J. Egyptian Math. Soc. 24, 263-269, 2016.
  • 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.
  • 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.
  • K. Yano and M. Kon, Anti-invariant submanifolds of a Sasakian space form, Tohoku Math. J. 29, 9-23, 1977.

Semiparallel Submanifolds of a Normal Paracontact Metric Manifold

Year 2019, Volume: 48 Issue: 2, 501 - 509, 01.04.2019

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.

References

  • 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.
  • 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.
  • 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.
  • 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.
  • A. Bejancu and N. Papaghuic, Semi-Invariant Submanifolds of a Sasakian space form, Collog. Math. 48, 77-88, 1984.
  • A. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosympectic man- ifold, Demonstratio Math. 19, 395-401, 1986.
  • I. Ishıhara, Anti-invariant submanifolds of a Sasakian space form, Kodai Math. J. 2, 171-186, 1979.
  • 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.
  • 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.
  • M. Kon, Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep. 25, 330-336, 1973.
  • C. Özgür, F. Gürler and C. Murathan, On semiparallel anti invariant submanifolds of generalized Sasakian space forms, Turk J. Math. 38, 796-802, 2014.
  • M.H. Shahid, Anti-invariant submanifolds of a Kenmotsu manifold, Kuwait J. Sci. Eng. 23 (2), 1996.
  • A.A. Shaikh, Y. Matsuyama and S.K. Hui, On invariant submanifolds of $(LCS)_n$−manifolds, J. Egyptian Math. Soc. 24, 263-269, 2016.
  • 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.
  • 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.
  • K. Yano and M. Kon, Anti-invariant submanifolds of a Sasakian space form, Tohoku Math. J. 29, 9-23, 1977.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Mehmet Atçeken 0000-0001-8665-5945

Ümit Yıldırım 0000-0002-7178-4223

Süleyman Dirik 0000-0001-9093-1607

Publication Date April 1, 2019
Published in Issue Year 2019 Volume: 48 Issue: 2

Cite

APA Atçeken, M., Yıldırım, Ü., & Dirik, S. (2019). Semiparallel Submanifolds of a Normal Paracontact Metric Manifold. Hacettepe Journal of Mathematics and Statistics, 48(2), 501-509.
AMA Atçeken M, Yıldırım Ü, Dirik S. Semiparallel Submanifolds of a Normal Paracontact Metric Manifold. Hacettepe Journal of Mathematics and Statistics. April 2019;48(2):501-509.
Chicago Atçeken, Mehmet, Ümit Yıldırım, and Süleyman Dirik. “Semiparallel Submanifolds of a Normal Paracontact Metric Manifold”. Hacettepe Journal of Mathematics and Statistics 48, no. 2 (April 2019): 501-9.
EndNote Atçeken M, Yıldırım Ü, Dirik S (April 1, 2019) Semiparallel Submanifolds of a Normal Paracontact Metric Manifold. Hacettepe Journal of Mathematics and Statistics 48 2 501–509.
IEEE M. Atçeken, Ü. Yıldırım, and S. Dirik, “Semiparallel Submanifolds of a Normal Paracontact Metric Manifold”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, pp. 501–509, 2019.
ISNAD Atçeken, Mehmet et al. “Semiparallel Submanifolds of a Normal Paracontact Metric Manifold”. Hacettepe Journal of Mathematics and Statistics 48/2 (April 2019), 501-509.
JAMA Atçeken M, Yıldırım Ü, Dirik S. Semiparallel Submanifolds of a Normal Paracontact Metric Manifold. Hacettepe Journal of Mathematics and Statistics. 2019;48:501–509.
MLA Atçeken, Mehmet et al. “Semiparallel Submanifolds of a Normal Paracontact Metric Manifold”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, 2019, pp. 501-9.
Vancouver Atçeken M, Yıldırım Ü, Dirik S. Semiparallel Submanifolds of a Normal Paracontact Metric Manifold. Hacettepe Journal of Mathematics and Statistics. 2019;48(2):501-9.