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On Contact CR-Submanifolds of a Kenmotsu Manifold

Year 2018, Volume: 10, 153 - 159, 29.12.2018

Abstract

In this paper, we study the dierential geometry of contact CR-submanifolds of a Kenmotsu manifold.
Necessary and sucient conditions are given for a submanifold to be a contact CR-submanifold in Kenmotsu
manifolds. Finally, the induced structures on submanifolds are investigated, these structures are categorized and we
discuss these results

References

  • Arslan, K., Ezentas, R., Mihai, I., Murathan, C., Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42(5)(2005), 1101-1110. 1
  • Atçeken, M., Contact CR-warped product submanifolds in cosymplectic space forms, Collect. Math., (2011), 62:1726 DOI 10.1007/s13348- 010-0002-z. 1
  • Atçeken, M., Contact CR-warped product submanifolds in cosymplectic manifolds, Kyungpook Math. J., 56(2016), 965-977. 1
  • Atçeken, M., Contact CR-submanifolds of Kenmotsu manifolds, Serdica Math. J., 37(2011), 67-78. 1
  • Atçeken, M., Dirik, S., Contact CR-submanifolds of Kenmotsu manifolds, Acta Univ. Sapientiae, Mathematica, 4(2)(2012), 182-198. 1, 3.2
  • Bejancu, A., Geometry of CR-submanifolds, Kluwer, Dortrecht (1986). 1
  • Bejancu, A., CR-submanifolds of a Kaehler manifold, Proc. Amer. Math. Soc., 69 (1978), 135-142. 1
  • Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509. Springer-Verlag, New York, (1976). 1
  • Blair, D. E., Chen, B.Y., On CR-submanifolds of Hermitian manifold, Israel Journal of Mathematics, 34 (1980), 353-363.
  • Dirik, S., On Contact CR-Submanifolds of a Cosymplectic Manifold, Filomat, 32 (14)(2018), In press. 3.10
  • Hasegawa, I., Mihai, I,. Contact CR-warped product submanifolds in Sasakian Manifolds, Geom. Dedicata, 102(2003), 143-150.
  • Hui, S. K., Mandal, P., Pseudo parallel contact CR-submanifolds of Kenmotsu manifolds, Indian Journal of Mathematics, 59(3)(2017), 385-402.
  • Kenmotsu, K., A Class of almost contact Riemannian manifold. Tohoku Math. J. 24 (1972), 93-103.
  • Matsumato, K., Contact CR-submanifolds of Sasakian manifolds, Internat. J. Math., 6(2)(1983), 303-326.
  • Uddin, S., Khan, K. A., Warped product CR-submanifolds of cosymplectic manifolds, Ricerche di Matematica, 60(1)(2011), 143-149.
  • Uddin, S., Khan, V. A., Khan, K. A., A note on warped product submanifolds of Cosymplectic manifolds, Filomat, 24(3)(2010), 95-102.
Year 2018, Volume: 10, 153 - 159, 29.12.2018

Abstract

References

  • Arslan, K., Ezentas, R., Mihai, I., Murathan, C., Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42(5)(2005), 1101-1110. 1
  • Atçeken, M., Contact CR-warped product submanifolds in cosymplectic space forms, Collect. Math., (2011), 62:1726 DOI 10.1007/s13348- 010-0002-z. 1
  • Atçeken, M., Contact CR-warped product submanifolds in cosymplectic manifolds, Kyungpook Math. J., 56(2016), 965-977. 1
  • Atçeken, M., Contact CR-submanifolds of Kenmotsu manifolds, Serdica Math. J., 37(2011), 67-78. 1
  • Atçeken, M., Dirik, S., Contact CR-submanifolds of Kenmotsu manifolds, Acta Univ. Sapientiae, Mathematica, 4(2)(2012), 182-198. 1, 3.2
  • Bejancu, A., Geometry of CR-submanifolds, Kluwer, Dortrecht (1986). 1
  • Bejancu, A., CR-submanifolds of a Kaehler manifold, Proc. Amer. Math. Soc., 69 (1978), 135-142. 1
  • Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509. Springer-Verlag, New York, (1976). 1
  • Blair, D. E., Chen, B.Y., On CR-submanifolds of Hermitian manifold, Israel Journal of Mathematics, 34 (1980), 353-363.
  • Dirik, S., On Contact CR-Submanifolds of a Cosymplectic Manifold, Filomat, 32 (14)(2018), In press. 3.10
  • Hasegawa, I., Mihai, I,. Contact CR-warped product submanifolds in Sasakian Manifolds, Geom. Dedicata, 102(2003), 143-150.
  • Hui, S. K., Mandal, P., Pseudo parallel contact CR-submanifolds of Kenmotsu manifolds, Indian Journal of Mathematics, 59(3)(2017), 385-402.
  • Kenmotsu, K., A Class of almost contact Riemannian manifold. Tohoku Math. J. 24 (1972), 93-103.
  • Matsumato, K., Contact CR-submanifolds of Sasakian manifolds, Internat. J. Math., 6(2)(1983), 303-326.
  • Uddin, S., Khan, K. A., Warped product CR-submanifolds of cosymplectic manifolds, Ricerche di Matematica, 60(1)(2011), 143-149.
  • Uddin, S., Khan, V. A., Khan, K. A., A note on warped product submanifolds of Cosymplectic manifolds, Filomat, 24(3)(2010), 95-102.
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Süleyman Dirik 0000-0001-9093-1607

Mehmet Atçeken 0000-0001-8665-5945

Ümit Yıdırım 0000-0002-7178-4223

Publication Date December 29, 2018
Published in Issue Year 2018 Volume: 10

Cite

APA Dirik, S., Atçeken, M., & Yıdırım, Ü. (2018). On Contact CR-Submanifolds of a Kenmotsu Manifold. Turkish Journal of Mathematics and Computer Science, 10, 153-159.
AMA Dirik S, Atçeken M, Yıdırım Ü. On Contact CR-Submanifolds of a Kenmotsu Manifold. TJMCS. December 2018;10:153-159.
Chicago Dirik, Süleyman, Mehmet Atçeken, and Ümit Yıdırım. “On Contact CR-Submanifolds of a Kenmotsu Manifold”. Turkish Journal of Mathematics and Computer Science 10, December (December 2018): 153-59.
EndNote Dirik S, Atçeken M, Yıdırım Ü (December 1, 2018) On Contact CR-Submanifolds of a Kenmotsu Manifold. Turkish Journal of Mathematics and Computer Science 10 153–159.
IEEE S. Dirik, M. Atçeken, and Ü. Yıdırım, “On Contact CR-Submanifolds of a Kenmotsu Manifold”, TJMCS, vol. 10, pp. 153–159, 2018.
ISNAD Dirik, Süleyman et al. “On Contact CR-Submanifolds of a Kenmotsu Manifold”. Turkish Journal of Mathematics and Computer Science 10 (December 2018), 153-159.
JAMA Dirik S, Atçeken M, Yıdırım Ü. On Contact CR-Submanifolds of a Kenmotsu Manifold. TJMCS. 2018;10:153–159.
MLA Dirik, Süleyman et al. “On Contact CR-Submanifolds of a Kenmotsu Manifold”. Turkish Journal of Mathematics and Computer Science, vol. 10, 2018, pp. 153-9.
Vancouver Dirik S, Atçeken M, Yıdırım Ü. On Contact CR-Submanifolds of a Kenmotsu Manifold. TJMCS. 2018;10:153-9.