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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.
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Sem. Rep. 25, 330-336, 1973.
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of generalized Sasakian space forms, Turk J. Math. 38, 796-802, 2014.
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A.A. Shaikh, Y. Matsuyama and S.K. Hui, On invariant submanifolds of
$(LCS)_n$−manifolds, J. Egyptian Math. Soc. 24, 263-269, 2016.
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submanifolds of cosymplectic manifolds, Rocky Mountain J. Math. 45 (1), 361-369,
2015.
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cosymplectic manifold, Hacet. J. Math. Stat. 43 (4), 635-640, 2014.
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Semiparallel Submanifolds of a Normal Paracontact Metric Manifold
Year 2019,
Volume: 48 Issue: 2, 501 - 509, 01.04.2019
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.
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.
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.