Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

Duggal, Krishan L.; Bejancu, Aurel

doi:10.1007/978-94-017-2089-2

Cited by 493 publications

(782 citation statements)

References 0 publications

Supporting

Mentioning

753

Contrasting

Unclassified

Order By: Relevance

“…After their book [18], many authors studied lightlike hypersurfaces by using their approach. In [27], Şahin introduced the notion of semisymmetric lightlike hypersurfaces of a semi-Riemannian manifold and obtained many new results.…”

Section: The Manifold (M G) Is Pseudosymmetric If Only If R · R = Lqmentioning

confidence: 99%

“…For the geometry of lightlike hypersurfaces, we refer to [18] and [19]. Let (M, g) be a hypersurface of a (m + 2) -dimensional, with g =ḡ |M ,…”

Section: Preliminariesmentioning

confidence: 99%

“…where RadT M is called radical distribution [18]. We also recall that the nullity degree of g for a lightlike hypersurface of M is 1.…”

Section: Preliminariesmentioning

confidence: 99%

“…) and C is a 1 -form on U defined by 18) for any X, Y, Z ∈ Γ(T M ) and N ∈ Γ(tr(T M )), where R is curvature tensor field of M .…”

Section: Preliminariesmentioning

confidence: 99%

See 3 more Smart Citations

Pseudosymmetric lightlike hypersurfaces

Kazan¹,

Şahin²

2014

Turk J Math

View full text Add to dashboard Cite

Abstract:We study lightlike hypersurfaces of a semi-Riemannian manifold satisfying pseudosymmetry conditions. We give sufficient conditions for a lightlike hypersurface to be pseudosymmetric and show that there is a close relationship of the pseudosymmetry condition of a lightlike hypersurface and its integrable screen distribution. We obtain that a pseudosymmetric lightlike hypersurface is a semisymmetric lightlike hypersurface or totally geodesic under certain conditions. Moreover, we give an example of pseudosymmetric lightlike hypersurfaces and investigate pseudoparallel lightlike hypersurfaces. Furthermore, we introduce Ricci-pseudosymmetric lightlike hypersurfaces, obtain characterizations, and give an example for such hypersurfaces.

show abstract

Section: The Manifold (M G) Is Pseudosymmetric If Only If R · R = Lqmentioning

confidence: 99%

“…For the geometry of lightlike hypersurfaces, we refer to [18] and [19]. Let (M, g) be a hypersurface of a (m + 2) -dimensional, with g =ḡ |M ,…”

Section: Preliminariesmentioning

confidence: 99%

See 2 more Smart Citations

Pseudosymmetric lightlike hypersurfaces

Kazan¹,

Şahin²

2014

Turk J Math

View full text Add to dashboard Cite

show abstract

“…Researchers use lightlike hypersurfaces in order to show a class of lightlike hypersurfaces came from the physically significant homegeneous spacetime manifolds of general relativity [2].…”

Section: Introductionmentioning

confidence: 99%