Constant curvature of a locally conformal almost cosymplectic manifold

Abood, Habeeb M.; Al-Hussaini, F.H.

doi:10.1063/1.5095088

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…In this section, we introduce a generalization of the notion of ACR-manifold of constant curvature that is used by Abood and Al-Hussaini [2]. We shall present this idea in the following definition: Definition 4.1.…”

Section: Generalized Curvature Tensor Related With Another Tensorsmentioning

confidence: 99%

Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu type

Abass¹,

Abood²

2023

Communications in Mathematics

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This paper determined the components of the generalized curvature tensor for the class of Kenmotsu type and established the mentioned class is {\eta}-Einstein manifold when the generalized curvature tensor is flat; the converse holds true under suitable conditions. It also introduced the notion of generalized {\Phi}-holomorphic sectional (G{\Phi}SH-) curvature tensor and thus found the necessary and sufficient conditions for the class of Kenmotsu type to be of constant G{\Phi}SH-curvature. In addition, the notion of {\Phi}-generalized semi-symmetric was introduced and its relationship with the class of Kenmotsu type and {\eta}-Einstein manifold established. Furthermore, this paper generalized the notion of the manifold of constant curvature and deduced its relationship with the aforementioned ideas. It finally showed that the class of Kenmotsu type exists as a hypersurface of the Hermitian manifold and derived a relation between the components of the Riemannian curvature tensors of the almost Hermitian manifold and its hypersurfaces.

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Section: Generalized Curvature Tensor Related With Another Tensorsmentioning

confidence: 99%

Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu type

Abass¹,

Abood²

2023

Communications in Mathematics

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“…On the other hand, Olszak [19] discovered the locally conformal almost (LCA-) cosymplectic manifolds in 1989. Later, many authors deal with the class of LCA-cosymplectic manifolds such as Massamba and Mavambou [18] and Abood and Al-Hussaini [7,8]. While, Kirichenko and Kharitonova [15] studied the normal class of LCA-cosymplectic manifolds.…”

Section: Introductionmentioning

confidence: 99%

Geometry of Locally Conformal C-12 Manifolds

Yusuf

2023

basjs

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This study deals with the class of locally conformal manifolds in such a way that the characterization identity for the aforementioned class is produced. Furthermore, the first clan of Cartan's structure equations is determined when the components of Kirichenko's tensors on associated G-structures for locally conformal manifolds are determined. The second clan of Cartan's structural equations for locally conformal manifolds was also completed.

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“…Taleshian et al [18] considered LP -Sasakian manifolds admitting a conharmonic curvature tensor. Abood and Al-Hussaini [3] studied the geometrical properties of the conharmonic tensor of a locally conformal almost cosymplectic manifold. In particular, the authors established the necessary and sufficient conditions for the conharmonic tensor to be flat, the aforementioned manifold to be normal and an η-Einstein manifold.…”

Section: Introductionmentioning

confidence: 99%

Quaisi invariant conharmonic tensor of special classes of locally conformal almost cosymplectic manifold

Al-Hussaini

Abood

2020

Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki

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The authors classified a locally conformal almost cosympleсtic manifold (LCAC S-manifold) according to the conharmonic curvature tensor. In particular, they have determined the necessary conditions for a conharmonic curvature tensor on the LCAC S-manifold of classes CT i , i = 1, 2, 3 to be Φ-quaisi invariant. Moreover, it has been proved that any LCAC S-manifold of the class CT 1 is conharmoniclly Φ-paracontact.

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Constant curvature of a locally conformal almost cosymplectic manifold

Cited by 3 publications

References 10 publications

Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu type

Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu type

Geometry of Locally Conformal C-12 Manifolds

Quaisi invariant conharmonic tensor of special classes of locally conformal almost cosymplectic manifold

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