Research Article
BibTex RIS Cite

Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds

Year 2021, Volume: 2 Issue: 1, 16 - 24, 09.07.2021

Toukeer Khan

Abstract

The object of this paper is to study non-invariant hypersurfaces of hyperbolic Sasakian manifolds equipped with (f,g,u,v,λ)- structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non -invariant hypersurfaces with (f,g,u,v,λ)- structure of hyperbolic Sasakian manifolds to be totally geodesic. The second fundamental form of a non-invariant hypersurface of hyperbolic Sasakian manifolds with (f,g,u,v,λ) - structure has been traced under the condition when f is parallel.

Keywords

totally geodesic totally umbilical Hyperbolic Sasakian manifold

References

  • Goldberg SI. Conformal transformation of Kaehler manifolds. Bulletin of American Mathematical Society. 1960. 66: 54-58.
  • Goldberg SI, Yano K. Non-invariant hypersurfaces of almost contact manifolds. Journal of the Mathematical Society of Japan. 1970. 22(1): 25-34.
  • Yano K, Okumura M. On (f,g,u,v,λ) – structures. Kodai Mathematical Seminar Reports. 1970. 22: 401-423.
  • Blair DE, Ludden GD. Hypersurfaces in Almost Contact Manifold, Tohoku Math. J. 1969. 22: 354-362.
  • Matsumoto K, Mihai I, Rosaca R. ξ-null geodesic vector fields on a LP-Sasakian manifold. J. Korean Math. Soc. 1995. 32: 17-31
  • Blair DE. Contact Manifolds in Riemannian Geometry. Lecture Notes in Mathematics vol. 509. Springer-Verlag: Berlin; 1976.
  • Chen BY. Geometry of submanifolds. Marcel Dekker: New York; 1973.
  • Sinha BB, Sharma R. Hypersurfaces in an almost paracontact manifold. Indian J. Pure App. Math. 1978. 9: 1083-1090.
  • Sarkar A, Sen M. On invariant submanifolds of trans-Sasakian manifolds. Pro. Estonian Acad. Sci. 2012. 61(1): 29-37.
  • Sular S, Ozgur C. On submanifolds of Kenmotsu manifolds. Chaos, Solitons and Fractals. 2009. 42: 1990-1995.
  • Khan T. On Non-invariant Hypersurfaces of a Nearly Kenmotsu Manifold. IOSR-JM. 2019. 15(6): 30-34. DOI: 10.9790/5728-1506013034.
  • Prasad R. On non-invariant hypersurfaces of trans-Sasakian manifolds. Bulletin of the Calcutta Mathematical Society. 2007. 99(5): 501-510.
  • Ahmed M, Khan SA, Khan T. On Non-invariant Hypersurfaces of a Nearly Hyperbolic Sasakian Manifold. International Journal of Mathematics. 2017.28(8): 1- 8. DOI: 10.1142/S0129167X17500641.
  • Upadhyay MD, Dubey KK. Almost hypersurfaces contact (f,ξ,η,g)-structure. Acta Mathematica Academaiae Scientairum Hyngrical Tomus. 28 H-1053, 13.15.

Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds

Year 2021, Volume: 2 Issue: 1, 16 - 24, 09.07.2021

Toukeer Khan

Abstract

The object of this paper is to study non-invariant hypersurfaces of hyperbolic Sasakian manifolds equipped with (f,g,u,v,λ)- structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non -invariant hypersurfaces with (f,g,u,v,λ)- structure of hyperbolic Sasakian manifolds to be totally geodesic. The second fundamental form of a non-invariant hypersurface of hyperbolic Sasakian manifolds with (f,g,u,v,λ) - structure has been traced under the condition when f is parallel.

Keywords

Totally geodesic Totally umbilical Hyperbolic Sasakian manifold

References

  • Goldberg SI. Conformal transformation of Kaehler manifolds. Bulletin of American Mathematical Society. 1960. 66: 54-58.
  • Goldberg SI, Yano K. Non-invariant hypersurfaces of almost contact manifolds. Journal of the Mathematical Society of Japan. 1970. 22(1): 25-34.
  • Yano K, Okumura M. On (f,g,u,v,λ) – structures. Kodai Mathematical Seminar Reports. 1970. 22: 401-423.
  • Blair DE, Ludden GD. Hypersurfaces in Almost Contact Manifold, Tohoku Math. J. 1969. 22: 354-362.
  • Matsumoto K, Mihai I, Rosaca R. ξ-null geodesic vector fields on a LP-Sasakian manifold. J. Korean Math. Soc. 1995. 32: 17-31
  • Blair DE. Contact Manifolds in Riemannian Geometry. Lecture Notes in Mathematics vol. 509. Springer-Verlag: Berlin; 1976.
  • Chen BY. Geometry of submanifolds. Marcel Dekker: New York; 1973.
  • Sinha BB, Sharma R. Hypersurfaces in an almost paracontact manifold. Indian J. Pure App. Math. 1978. 9: 1083-1090.
  • Sarkar A, Sen M. On invariant submanifolds of trans-Sasakian manifolds. Pro. Estonian Acad. Sci. 2012. 61(1): 29-37.
  • Sular S, Ozgur C. On submanifolds of Kenmotsu manifolds. Chaos, Solitons and Fractals. 2009. 42: 1990-1995.
  • Khan T. On Non-invariant Hypersurfaces of a Nearly Kenmotsu Manifold. IOSR-JM. 2019. 15(6): 30-34. DOI: 10.9790/5728-1506013034.
  • Prasad R. On non-invariant hypersurfaces of trans-Sasakian manifolds. Bulletin of the Calcutta Mathematical Society. 2007. 99(5): 501-510.
  • Ahmed M, Khan SA, Khan T. On Non-invariant Hypersurfaces of a Nearly Hyperbolic Sasakian Manifold. International Journal of Mathematics. 2017.28(8): 1- 8. DOI: 10.1142/S0129167X17500641.
  • Upadhyay MD, Dubey KK. Almost hypersurfaces contact (f,ξ,η,g)-structure. Acta Mathematica Academaiae Scientairum Hyngrical Tomus. 28 H-1053, 13.15.
There are 14 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Toukeer Khan This is me

Publication Date July 9, 2021
Submission Date June 1, 2021
Published in Issue Year 2021 Volume: 2 Issue: 1

Cite

APA Khan, T. (2021). Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds. Bingöl Üniversitesi Teknik Bilimler Dergisi, 2(1), 16-24.
AMA Khan T. Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds. BUTS. July 2021;2(1):16-24.
Chicago Khan, Toukeer. “Non-Invariant Hypersurfaces of Hyperbolic Sasakian Manifolds”. Bingöl Üniversitesi Teknik Bilimler Dergisi 2, no. 1 (July 2021): 16-24.
EndNote Khan T (July 1, 2021) Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds. Bingöl Üniversitesi Teknik Bilimler Dergisi 2 1 16–24.
IEEE T. Khan, “Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds”, BUTS, vol. 2, no. 1, pp. 16–24, 2021.
ISNAD Khan, Toukeer. “Non-Invariant Hypersurfaces of Hyperbolic Sasakian Manifolds”. Bingöl Üniversitesi Teknik Bilimler Dergisi 2/1 (July 2021), 16-24.
JAMA Khan T. Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds. BUTS. 2021;2:16–24.
MLA Khan, Toukeer. “Non-Invariant Hypersurfaces of Hyperbolic Sasakian Manifolds”. Bingöl Üniversitesi Teknik Bilimler Dergisi, vol. 2, no. 1, 2021, pp. 16-24.
Vancouver Khan T. Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds. BUTS. 2021;2(1):16-24.
 Download Cover Image
This journal is prepared and published by the Bingöl University Technical Sciences journal team.