Null Curves and Hypersurfaces of Semi-Riemannian Manifolds

Duggal, Krishan L.; Jin, Dae Ho

doi:10.1142/6449

Cited by 182 publications

(227 citation statements)

References 54 publications

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“…In general, R (0, 2) is not symmetric [1,2]. If R (0, 2) is symmetric, then it is called the induced Ricci tensor of M and denote it by Ric.…”

Section: Dae Ho Jinmentioning

confidence: 99%

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Ascreen Lightlike Hypersurfaces of an Indefinite Sasakian Manifold

Jin¹

2013

The Pure and Applied Mathematics

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“…In general, R (0, 2) is not symmetric [1,2]. If R (0, 2) is symmetric, then it is called the induced Ricci tensor of M and denote it by Ric.…”

Section: Dae Ho Jinmentioning

confidence: 99%

“…The study of such notion was initiated by Duggal and Bejancu [1] and later studied by many authors (see up-to date results in two books [2,5]). Recently several authors studied the geometry of lightlike submanifolds of indefinite Sasakian manifolds [3,4,6,9].…”

Section: Introductionmentioning

confidence: 99%

Ascreen Lightlike Hypersurfaces of an Indefinite Sasakian Manifold

Jin¹

2013

The Pure and Applied Mathematics

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“…As the shape operator is an information tool in studying the geometry of submanifolds, their studying turns out very important. For instance, in [5] a class of lightlike hypersurfaces whose shape operators are the same as the one of their screen distribution up to a conformal non zero smooth factor in F(M) was considered. That work gave a way to generate, under some geometric conditions, an integrable canonical screen (see [5] for more details).…”

Section: By Theorem 23 In [4] Page 89 the Screen Distribution S(tm)mentioning

confidence: 99%

“…They introduced a non-degenerate screen distribution to construct a nonintersecting lightlike transversal vector bundle of the tangent bundle. Several authors have studied lightlike hypersurfaces of semi-Riemannian manifolds (see [5] and many more references therein).…”

Section: Introductionmentioning

confidence: 99%

Lightlike Geometry of Leaves in Indefinite Kenmotsu Manifolds

Massamba

2011

Cubo

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In this paper, we study some aspects of the geometry of leaves of integrable distributions of lightlike hypersurfaces in indefinite Kenmotsu manifolds, tangent to the structure vector field. Theorems on parallel vector field, Killing distribution, geodesibility of lightlike hypersurfaces are obtained. Some characterization Theorems of leaves of integrable distributions are given. We prove that there exists a distribution, subset of the screen distribution, in which, under the integrability condition, any totally contact umbilical leaf is an extrinsic sphere. RESUMENEn este trabajo se estudian algunos aspectos de la geometría de las hojas de distribuciones integrables de las hipersuperficies luminosas en variedades de Kenmotsu indefinidas, tangentes a la estructura de un campo vectorial. Se obtienen algunos teoremas sobre el campo de vectores paralelo, distribución de Killing y geodesbilidad de hipersuperficies liminosas. Se dan algunos teoremas de caracterización de las hojas de las distribuciones integrables. Se demuestra que existe una distribucin, subconjunto de 70 Fortuné Massamba CUBO 13, 3 (2011) la distribucin de la pantalla, en la que, bajo la condición de integrabilidad, cualquier contacto con la hoja umbilical es una esfera extrínseca.

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“…Many mathematical and physical scientists who study the theories of general relativity and classical string emphasized the importance of the null curves in recent years ( [6,9,10,13,14,15,16,17,18]). …”

Section: Introductionmentioning

confidence: 99%