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A Note on Nearly Hyperbolic Cosymplectic Manifolds

Year 2020, Volume: 23 Issue: 4, 1403 - 1406, 01.12.2020
https://doi.org/10.2339/politeknik.765076

Abstract

Interest in hyperbolic cosymplectic manifolds has increased in recent years. In this paper, pseudo slant submanifolds of a nearly hyperbolic cosymplectic manifold have been explored deeply. In particular, the integrability conditions of distributions on such manifolds have been investigated. So, for a pseudo submanifold M of a nearly hyperbolic cosymplectic manifold M ̃ which is totally geodesic, D_θ,D_( _μ ) distributions with〖 D〗_( _μ )⊕⟨ξ⟩ and D_θ⊕D_( _μ ) are proved integrable but D_( _θ )⊕⟨ξ⟩ or not.

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Thanks

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References

  • [1] Upadhyay M.D., Dube K.K., “Almost contact hyperbolic (f,g,η,ξ)-structure”. Acta Math. Acad. Sci. Hungary, 28(1-2): 1–4, (1976).
  • [2] Joshi N. K., Dube K. K., “Semi-invariant submanifold of an almost r-contact hyperbolic metric manifold”. Demonstratio Math., 34(1): 135–143, (2001).
  • [3] Dogan S., Karadag, M., “Slant submanifolds of an almost hyperbolic contact metric manifolds”. Journal of Mathematics and System Science, 4: 285–288, (2014).
  • [4] Uddin S., Wong B. R., Mustafa A. A., “Warped product pseudo slant submanifolds of a nearly cosymplectic manifold”. Abstr. Appl. Anal., Art. ID 420890, 1-13, (2012).
  • [5] Ahmad M., Ali K., “Semi-invariant Submanifolds of Nearly Hyperbolic Cosymplectic Manifolds”. Global Journal of Science Frontier Research Mathematics and Decision Sciences, 13(4), 73–81, (2013).
  • [6] Ahmad M., Ali K., “CR-submanifolds of a nearly hyperbolic cosymplectic manifold”. IOSR Journal of Mathematics (IOSR-JM), 6(3): 74–77, (2013).
  • [7] Khan V. A., Khan M. A., “Pseudo Slant Submanifolds of a Sasakian Manifold”. Indian J. Pure Appl. Math., 38(1): 31–42, (2007).
  • [8] De U. C., Sarkar A., “On pseudo slant submanifolds of Trans-Sasakian Manifolds”. Proc. Est. Acad. Sci., 60(1): 1–11, (2011).
  • [9] Blair D.E., “Riemannian Geometry of contact and symplectic manifolds”, Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston , MA, 2002
  • [10] Fujumoto A., Muto H., “On Cosymplectic manifolds”,Tensor N.S., 28:43-52,(1974).
  • [11] Olszak Z., “On almost Cosymplectic manifolds”. Kodai Math. J., 4:239-250,(1981),
  • [12] Koufogiorgos Th., Tsiclias C., “On the existense of a new class of contact metric manifolds”.Canad. Math. Bull., 43:440-447,(2000).
  • [13] Baikoussis C., Koufogiorgos T., “On a type of contact manifolds”. J. Geom. 46:1-9,(1993).
  • [14] Endo H., “On some properties of almost Cosymplectic manifolds”, An Ştiint.Univ. ‘’Al.I.Cuza’’ Iaşi, Math.42: 79-94, (1996).
  • [15].Goldberg S.I., Yano K., “Integrability of almost cosymplectic structures”. Pasific J.Math.31: 373-382, (1969).

A Note on Nearly Hyperbolic Cosymplectic Manifolds

Year 2020, Volume: 23 Issue: 4, 1403 - 1406, 01.12.2020
https://doi.org/10.2339/politeknik.765076

Abstract

Interest in hyperbolic cosymplectic manifolds has increased in recent years. In this paper, pseudo slant submanifolds of a nearly hyperbolic cosymplectic manifold have been explored deeply. In particular, the integrability conditions of distributions on such manifolds have been investigated. So, for a pseudo submanifold M of a nearly hyperbolic cosymplectic manifold M ̃ which is totally geodesic, D_θ,D_( _μ ) distributions with〖 D〗_( _μ )⊕⟨ξ⟩ and D_θ⊕D_( _μ ) are proved integrable but D_( _θ )⊕⟨ξ⟩ or not.

Project Number

-

References

  • [1] Upadhyay M.D., Dube K.K., “Almost contact hyperbolic (f,g,η,ξ)-structure”. Acta Math. Acad. Sci. Hungary, 28(1-2): 1–4, (1976).
  • [2] Joshi N. K., Dube K. K., “Semi-invariant submanifold of an almost r-contact hyperbolic metric manifold”. Demonstratio Math., 34(1): 135–143, (2001).
  • [3] Dogan S., Karadag, M., “Slant submanifolds of an almost hyperbolic contact metric manifolds”. Journal of Mathematics and System Science, 4: 285–288, (2014).
  • [4] Uddin S., Wong B. R., Mustafa A. A., “Warped product pseudo slant submanifolds of a nearly cosymplectic manifold”. Abstr. Appl. Anal., Art. ID 420890, 1-13, (2012).
  • [5] Ahmad M., Ali K., “Semi-invariant Submanifolds of Nearly Hyperbolic Cosymplectic Manifolds”. Global Journal of Science Frontier Research Mathematics and Decision Sciences, 13(4), 73–81, (2013).
  • [6] Ahmad M., Ali K., “CR-submanifolds of a nearly hyperbolic cosymplectic manifold”. IOSR Journal of Mathematics (IOSR-JM), 6(3): 74–77, (2013).
  • [7] Khan V. A., Khan M. A., “Pseudo Slant Submanifolds of a Sasakian Manifold”. Indian J. Pure Appl. Math., 38(1): 31–42, (2007).
  • [8] De U. C., Sarkar A., “On pseudo slant submanifolds of Trans-Sasakian Manifolds”. Proc. Est. Acad. Sci., 60(1): 1–11, (2011).
  • [9] Blair D.E., “Riemannian Geometry of contact and symplectic manifolds”, Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston , MA, 2002
  • [10] Fujumoto A., Muto H., “On Cosymplectic manifolds”,Tensor N.S., 28:43-52,(1974).
  • [11] Olszak Z., “On almost Cosymplectic manifolds”. Kodai Math. J., 4:239-250,(1981),
  • [12] Koufogiorgos Th., Tsiclias C., “On the existense of a new class of contact metric manifolds”.Canad. Math. Bull., 43:440-447,(2000).
  • [13] Baikoussis C., Koufogiorgos T., “On a type of contact manifolds”. J. Geom. 46:1-9,(1993).
  • [14] Endo H., “On some properties of almost Cosymplectic manifolds”, An Ştiint.Univ. ‘’Al.I.Cuza’’ Iaşi, Math.42: 79-94, (1996).
  • [15].Goldberg S.I., Yano K., “Integrability of almost cosymplectic structures”. Pasific J.Math.31: 373-382, (1969).
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Müge Karadağ 0000-0002-5722-5441

Project Number -
Publication Date December 1, 2020
Submission Date July 6, 2020
Published in Issue Year 2020 Volume: 23 Issue: 4

Cite

APA Karadağ, M. (2020). A Note on Nearly Hyperbolic Cosymplectic Manifolds. Politeknik Dergisi, 23(4), 1403-1406. https://doi.org/10.2339/politeknik.765076
AMA Karadağ M. A Note on Nearly Hyperbolic Cosymplectic Manifolds. Politeknik Dergisi. December 2020;23(4):1403-1406. doi:10.2339/politeknik.765076
Chicago Karadağ, Müge. “A Note on Nearly Hyperbolic Cosymplectic Manifolds”. Politeknik Dergisi 23, no. 4 (December 2020): 1403-6. https://doi.org/10.2339/politeknik.765076.
EndNote Karadağ M (December 1, 2020) A Note on Nearly Hyperbolic Cosymplectic Manifolds. Politeknik Dergisi 23 4 1403–1406.
IEEE M. Karadağ, “A Note on Nearly Hyperbolic Cosymplectic Manifolds”, Politeknik Dergisi, vol. 23, no. 4, pp. 1403–1406, 2020, doi: 10.2339/politeknik.765076.
ISNAD Karadağ, Müge. “A Note on Nearly Hyperbolic Cosymplectic Manifolds”. Politeknik Dergisi 23/4 (December 2020), 1403-1406. https://doi.org/10.2339/politeknik.765076.
JAMA Karadağ M. A Note on Nearly Hyperbolic Cosymplectic Manifolds. Politeknik Dergisi. 2020;23:1403–1406.
MLA Karadağ, Müge. “A Note on Nearly Hyperbolic Cosymplectic Manifolds”. Politeknik Dergisi, vol. 23, no. 4, 2020, pp. 1403-6, doi:10.2339/politeknik.765076.
Vancouver Karadağ M. A Note on Nearly Hyperbolic Cosymplectic Manifolds. Politeknik Dergisi. 2020;23(4):1403-6.