Bazı Tipteki Null Hiperyüzeyler

Year 2019, Volume: 7 Issue: 1, 33 - 38, 15.01.2019

Bilal Eftal Acet

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.

Keywords

Para-Sasakian manifold , Null Hiperyüzeyler , Lie re-current

Some Types of Null Hypersurfaces

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.

Keywords

Para-Sasakian manifold , Screen semi invariant null hypersurfaces , Screen totally geodesic null 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.