Curvature of indefinite almost contact manifolds

Bonome, A.; Castro, R.; Garcı́a-Rı́o, Eduardo; Hervella, Luis

doi:10.1007/bf01222928

Cited by 12 publications

(7 citation statements)

References 13 publications

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“…Then (φ, ξ, η, g) is called an indefinite almost contact metric structure on M if (φ, ξ, η) is an almost contact structure on M and g is a semi-Riemannian metric on M such that [4], for any vector field X, Y on M ,…”

Section: Preliminariesmentioning

confidence: 99%

Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds

Massamba

Ssekajja

2016

Arab. J. Math.

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In this paper, we introduce and study a new class of CR-lightlike submanifold of an indefinite nearly Sasakian manifold, called quasi generalized Cauchy-Riemann (QGCR) lightlike submanifold. We give some characterization theorems for the existence of QGCR-lightlike submanifolds and finally derive necessary and sufficient conditions for some distributions to be integrable. Mathematics Subject Classification

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Section: Preliminariesmentioning

confidence: 99%

Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds

Massamba

Ssekajja

2016

Arab. J. Math.

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“…Since φσ = σ, the φ-section σ is a holomorphic φ-section and the sectional curvature of a φ-section σ is called a φ-holomorphic sectional curvature (see [4]), [9] and references therein for more details). If a Kenmotsu manifold M has constant φ-holomorphic sectional curvature c, then, by virtue of the Proposition 12 in [10], the curvature tensor R of M is given by, for any X, Y , Z ∈ Γ(T M ),…”

Section: Preliminariesmentioning

confidence: 99%

“…Note that the φ-holomorphic sectional curvature of an indefinite C(α)-manifold does not satisfy, in general, a "Schur Lemma" although it holds for co-Kähler and indefinite Sasakian manifolds (see [4] for details).…”

Section: Preliminariesmentioning

confidence: 99%

On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds

Massamba

2009

J. Geom.

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We study semi-parallel lightlike hypersurfaces of an indefinite Kenmotsu manifold, tangent to the structure vector field. Some Theorems on parallel and semi-parallel vector field, geodesibility of lightlike hypersurfaces are obtained. The geometrical configuration of such lightlike hypersurfaces is established. We prove that, in totally contact umbilical lightlike hypersurfaces of an indefinite Kenmotsu manifold which has constant φ-holomorphic sectional curvature c, tangent to the structure vector field and such that its distribution is parallel, the parallelism and semi-parallelism notions are equivalent.Mathematics Subject Classification (2010). Primary 53C15; Secondary 53C25, 53C40, 53C50.

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“…Note that the φ-holomorphic sectional curvature of an indefinite C(α)-manifold does not satisfy, in general, a "Schur Lemma" although it holds for coKähler and indefinite Sasakian manifolds (see [3] for details).…”

Section: Preliminariesmentioning

confidence: 99%

“…Since φσ = σ, the φ-section σ is a holomorphic φ-section and the sectional curvature of a φ-section σ is called a φ-holomorphic sectional curvature (see [3], [11] and references therein for more details). If a Kenmotsu manifold M has constant φ-holomorphic sectional curvature c, then, by virtue of the Proposition 12 in [12], the Riemann curvature tensor R of M is given by, for any X, Y , Z ∈ Γ(T M ),…”

Section: Preliminariesmentioning

confidence: 99%

Equivalence Conditions of Symmetry Properties in Lightlike Hypersurfaces of Indefinite Kenmotsu Manifolds

Lungiambudila¹,

Massamba²,

Tossa³

2016

Bulletin of the Korean Mathematical Society

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Abstract. The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant φ-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hypersurfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hypersurfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.

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Curvature of indefinite almost contact manifolds

Cited by 12 publications

References 13 publications

Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds

Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds

On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds

Equivalence Conditions of Symmetry Properties in Lightlike Hypersurfaces of Indefinite Kenmotsu Manifolds

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