Lightlike hypersurfaces with planar normal sections in R₁⁴

Yıl 2020, Cilt: 69 Sayı: 1, 336 - 346, 30.06.2020

Selcen Yüksel Perktaş Feyza Esra Erdoğan

https://doi.org/10.31801/cfsuasmas.473923

Öz

In the present paper our aim is to investigate lightlike hypersurfaces of $\mathbb{R}^4_1$ having degenerate or non-degenerate planar normal sections.

Firstly, we prove that as lightlike hypersurfaces in $\mathbb{R}^4_1$ always has degenerate planar normal

sections. Then we examine the conditions for lightlike hypersurfaces in $\mathbb{R}^4_1$ to have non-degenerate planar normal

sections and obtain some characterizations for such lightlike hypersurfaces.

Anahtar Kelimeler

Lightlike hypersurface, non-degenerate planar normal section, degenerate normal section

Kaynakça

• Atindogbe, C. and Duggal, K. L., Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math. 11(4), (2004), 421-442.
• Chen, B. Y., Classification of hypersurfaces with Planar Normal Sections, Journal of Geometry, Vol.20 (1983), 122-127.
• Duggal, K. L. and Bejancu, A., Lightlike hypersurfaces of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publisher, 1996.
• Duggal, K. L. and Jin, D. H., Null Curves and hypersurfaces of Semi Riemannian Manifolds, World Scientific, 2007.
• Duggal, K. L. and Şahin B., Differential Geometry of Lightlike hypersurfaces, Springer Birkhauser, 2010.
• Kim, Y. H., Minimal hypersurfaces of pseudo-Euclidean spaces with geodesic normal sections, Differential Geometry and its Applications, 5 (1995), 321-329.
• Kim, Y. H., Pseudo-Riemannian hypersurfaces with pointwise planar normal sections, Math. J. Okayama Univ., 34 (1992), 249-257.
• Kim, Y. H., Hypersurfaces in a pseudo-Euclidean space with planar normal sections, Journal of Geometry, vol.35 (1989), 120-131.
• Li. S. J., Hypersurfaces with Pointwise Planar Normal Sections in a sphere, Journal of Geometry, 70 (2001), 101-107.
• O'Neill, B., Semi Riemannian Geometry with Applications to Relativity, Academic Press, 1983.
• Erdoğan, F. E., Güneş, R. and Şahin, B., Half-lightlike hypersurface with planar normal sections in R₂⁴, Turk. J. Math. Vol.38 (2014), 764-777.
• Erdoğan, F. E., Şahin, B. and Güneş, R., Lightlike hypersurfaces with planar normal section in Minkowski 3-space, Int. Electron. J. Geom., Vol.7, no.1, 2014.
• Erdoğan, F. E., Yüksel Perktaş, S. and Güneş, R. , Half Lightlike hypersurfaces with degenerate and non-degenerate planar normal sections in pseudo-Euclidean spaces, International Journal of Geometry, Vol. 7, No.1 (2018), 37-53.