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Bazı Tipteki Null Hiperyüzeyler

Year 2019, Volume: 7 Issue: 1, 33 - 38, 15.01.2019
https://doi.org/10.21541/apjes.347733

Abstract

Bu makalemizde, bir para-Sasakian manifoldun re-current, Lie re-current ve Hopf olarak adlandırılan üç tipteki null hiperyüzeyleri tanımlandı ve çalışıldı. Ayrıca bu tipteki null hiperyüzeyler için bazı sonuçlar elde edildi.

References

  • K.L. Duggal and A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and Its Applications (1996), Kluwer Publisher.
  • K.L. Duggal and B. Şahin, Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hungarica 112 (2006), 107-130.
  • K. L. Duggal and B. Şahin, “Lightlike submanifolds of indefinite Sasakian manifolds”, Int. J. Math. and Math. Sci., Article ID 57585, 2007.
  • K.L. Duggal and B. Şahin, Differential geometry of lightlike submanifolds, (2010), Frontiers in Mathematics.
  • G.J. Galloway, Lecture notes on spacetime geometry, Beijing Int. Math. Research Center (2007), 1-55.
  • B. E. Acet, S. Yüksel Perktaş and E. Kılıç, “Symmetric lightlike hypersurfaces of a para-Sasakian space form”, Analele Stiintifice Ale Universitatii Al. I. Cuza Iasi (N.S.), vol 2, pp. 915-926, 2016.
  • R. Kumar and R. K. Nagaich, “Characteriztion of GCR-lightlike warped product of indefinite cosympletic manifolds”, Novi Sad J. Math.,vol 42, pp. 111-126, 2012.
  • D. H. Jin, “Special lightlike hypersurfaces of indefinite Kaehler manifolds”, Filomat, vol 30, pp. 1919-1930, 2016.
  • D. H. Jin, “Lightlike hypersurfaces of indefinite Kaehler manifolds with a semi-symmetric non-metric connection”, J. Korean Math. Soc., vol 54, pp. 101-119, 2017
  • S. Kaneyuki and M. Konzai, Paracomplex structure and affine symmetric spaces, Tokyo J. Math. 8 (1985), 301-308.
  • S. Zamkovoy, Canonical connection on paracontact manifolds, Ann. Glob. Anal. Geo. 36 (2009), 37-60.
  • D.V. Alekseevski, C. Medori and A. Tomassini, Maximally homogeneous para-CR manifolds, Ann. Global Anal. Geom. 30 (2006), 1-27.
  • B.E. Acet, S. Yüksel Perktaş and E. Kılıç, On submanifolds of para-Sasakian manifolds, JP Journal of Geometry and Topology 19 (2016), 1-18.
  • V. Cortes, M.A. Lawn and L. Schafer, Affine hyperspheres associated to special para-Kaehler manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), 995-1009.
  • S. Erdem, On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (φ, φ′)- holomorphic maps between them, Houston J. Math. 28 (2002), 21-45.
  • S. Yüksel Perktaş, On para-Sasakian manifolds satisfying certain curvature conditions with canonical paracontact connection, Khayyam J. Math. 3 (2017), 34-44.
  • B. E. Acet, S. Yüksel Perktaşand E. Kılıç, “On lightlike geometry of para-Sasakian manifolds”, Scientific Work J., Article ID 696231, 2014.

Some Types of Null Hypersurfaces

Year 2019, Volume: 7 Issue: 1, 33 - 38, 15.01.2019
https://doi.org/10.21541/apjes.347733

Abstract

In this article, we introduce and study three types of
null hypersurfaces of a para-Sasakian manifold which are called re-current, Lie
re-current and Hopf null hypersurfaces. Also, we obtain some results on such
hypersurfaces.

References

  • K.L. Duggal and A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and Its Applications (1996), Kluwer Publisher.
  • K.L. Duggal and B. Şahin, Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hungarica 112 (2006), 107-130.
  • K. L. Duggal and B. Şahin, “Lightlike submanifolds of indefinite Sasakian manifolds”, Int. J. Math. and Math. Sci., Article ID 57585, 2007.
  • K.L. Duggal and B. Şahin, Differential geometry of lightlike submanifolds, (2010), Frontiers in Mathematics.
  • G.J. Galloway, Lecture notes on spacetime geometry, Beijing Int. Math. Research Center (2007), 1-55.
  • B. E. Acet, S. Yüksel Perktaş and E. Kılıç, “Symmetric lightlike hypersurfaces of a para-Sasakian space form”, Analele Stiintifice Ale Universitatii Al. I. Cuza Iasi (N.S.), vol 2, pp. 915-926, 2016.
  • R. Kumar and R. K. Nagaich, “Characteriztion of GCR-lightlike warped product of indefinite cosympletic manifolds”, Novi Sad J. Math.,vol 42, pp. 111-126, 2012.
  • D. H. Jin, “Special lightlike hypersurfaces of indefinite Kaehler manifolds”, Filomat, vol 30, pp. 1919-1930, 2016.
  • D. H. Jin, “Lightlike hypersurfaces of indefinite Kaehler manifolds with a semi-symmetric non-metric connection”, J. Korean Math. Soc., vol 54, pp. 101-119, 2017
  • S. Kaneyuki and M. Konzai, Paracomplex structure and affine symmetric spaces, Tokyo J. Math. 8 (1985), 301-308.
  • S. Zamkovoy, Canonical connection on paracontact manifolds, Ann. Glob. Anal. Geo. 36 (2009), 37-60.
  • D.V. Alekseevski, C. Medori and A. Tomassini, Maximally homogeneous para-CR manifolds, Ann. Global Anal. Geom. 30 (2006), 1-27.
  • B.E. Acet, S. Yüksel Perktaş and E. Kılıç, On submanifolds of para-Sasakian manifolds, JP Journal of Geometry and Topology 19 (2016), 1-18.
  • V. Cortes, M.A. Lawn and L. Schafer, Affine hyperspheres associated to special para-Kaehler manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), 995-1009.
  • S. Erdem, On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (φ, φ′)- holomorphic maps between them, Houston J. Math. 28 (2002), 21-45.
  • S. Yüksel Perktaş, On para-Sasakian manifolds satisfying certain curvature conditions with canonical paracontact connection, Khayyam J. Math. 3 (2017), 34-44.
  • B. E. Acet, S. Yüksel Perktaşand E. Kılıç, “On lightlike geometry of para-Sasakian manifolds”, Scientific Work J., Article ID 696231, 2014.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Bilal Eftal Acet

Publication Date January 15, 2019
Submission Date October 30, 2017
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

IEEE B. E. Acet, “Some Types of Null Hypersurfaces”, APJES, vol. 7, no. 1, pp. 33–38, 2019, doi: 10.21541/apjes.347733.