Lightlike Osserman submanifolds of semi-Riemannian manifolds

Atindogbé, Cyriaque; Lungiambudila, Oscar; Tossa, J.

doi:10.1007/s13370-011-0015-0

Cited by 6 publications

(9 citation statements)

References 16 publications

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“…Proof. The result hold from Theorem 3.2 in [9] and proposition 4. In case of coisotropic warped product of a semi-Riemannian manifold with constant sectional curvature which is conformal screen, we establish the following.…”

Section: Our Main Resultssupporting

confidence: 53%

Algebraicity of Induced Riemannian Curvature Tensor on Lightlike Warped Product Manifolds

Ndayirukiye¹,

Nibaruta²,

Karimumuryango³

et al. 2019

JAMP

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Lightlike warped product manifolds are considered in this paper. The geometry of lightlike submanifolds is difficult to study since the normal vector bundle intersects with the tangent bundle. Due to the degenerate metric, the induced connection is not metric and it follows that the Riemannian curvature tensor is not algebraic. In this situation, some basic techniques of calulus are not useable. In this paper, we consider lightlike warped product as submanifold of semi-Riemannian manifold and establish some remarkable geometric properties from which we establish some conditions on the algebraicity of the induced Riemannian curvature tensor.

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Section: Our Main Resultssupporting

confidence: 53%

Algebraicity of Induced Riemannian Curvature Tensor on Lightlike Warped Product Manifolds

Ndayirukiye¹,

Nibaruta²,

Karimumuryango³

et al. 2019

JAMP

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“…On lightlike geometry of hypersurfaces, C. Atindogbe and K. L. Duggal have studied Pseudo-Jacobi operators and considered Osserman conditions [8], and in [9], the authors introduced the notion of r-lightlike Osserman…”

Section: R T M ∈⊗mentioning

confidence: 99%

“…From Proposition 2, theorem 5 in [12] and Theorem 4.3 in [9], we proved the following result that characterizes any screen distribution of a coisotropic warped product of a semi-Riemannian space form with the first factor totally null. This case consists of a class of null warped products that is Einstein and pointwise Osserman.…”

mentioning

confidence: 91%

Osserman Conditions in Lightlike Warped Product Geometry

Ndayirukiye¹,

Nibirantiza²,

Nibaruta³

et al. 2020

JAMP

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In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study of lightlike warped product Osserman manifolds. For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product.

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“…Namely, according to the notation of [1,3,6,16,20], let S − p (M ), S + p (M ) and S p (M ) denote the sets of unit timelike, unit spacelike, and nonnull vectors in T p M , p ∈ M , respectively: …”

Section: Osserman Lightlike Hypersurfacesmentioning

confidence: 99%

Osserman lightlike hypersurfaces of indefinite $\mathcal S$-manifolds

Brunetti¹

2014

Turk J Math

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We mainly deal with the problem of admissibility for screen distributions on a lightlike hypersurface of both a semi-Riemannian manifold and an indefinite S -manifold. In the latter case, we first show that a characteristic screen distribution is never admissible, and then we provide a characterization for admissible screen distributions on proper totally umbilical lightlike hypersurfaces. Finally, in studying Osserman conditions, we characterize Osserman totally umbilical hypersurfaces of a semi-Riemannian manifold, obtaining explicit results on the eigenvalues of the pseudo-Jacobi operators in the case of lightlike hypersurfaces with Lorentzian screen leaves.

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Lightlike Osserman submanifolds of semi-Riemannian manifolds

Cited by 6 publications

References 16 publications

Algebraicity of Induced Riemannian Curvature Tensor on Lightlike Warped Product Manifolds

Algebraicity of Induced Riemannian Curvature Tensor on Lightlike Warped Product Manifolds

Osserman Conditions in Lightlike Warped Product Geometry

Osserman lightlike hypersurfaces of indefinite $\mathcal S$-manifolds

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