On curvature characterizations of some hypersurfaces in spaces of constant curvature

Sawicz, Katarzyna

doi:10.2298/pim0693095s

Cited by 16 publications

(16 citation statements)

References 12 publications

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“…where ψ and ρ are some functions on U H . We refer to [31,33,37,73,74,75,76,77] for results on hypersurfaces satisfying (1.17). Evidently, if M is a hypersurface in an 4-dimensional Riemannian space of constant curvature N 4 (c) then (1.17…”

Section: Pseudosymmetry Type Curvature Conditionsmentioning

confidence: 99%

Hypersurfaces in space forms satisfying some generalized Einstein metric condition

Deszcz¹,

Głogowska²,

Zafindratafa³

2018

Preprint

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The difference tensor C • R − R • C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n ≥ 4, satisfy the following curvature condition:We investigate hypersurfaces M in space forms N satisfying ( * ). The main result states that if the tensor C • R − R • C of a non-quasi-Einstein hypersurface M in N is a linear combination of the tensors Q(g, C) and Q(S, C) then ( * ) holds on M. In the case when M is a quasi-Einstein hypersurface in N and some additional assumptions are satisfied then ( * ) also holds on M. 1

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Section: Pseudosymmetry Type Curvature Conditionsmentioning

confidence: 99%

Hypersurfaces in space forms satisfying some generalized Einstein metric condition

Deszcz¹,

Głogowska²,

Zafindratafa³

2018

Preprint

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“…In particular, if R · R = L R Q(g, R) (resp., R · S = L S Q(g, S)) then the manifold is called Deszcz pseudosymmetric (resp., Ricci pseudosymmetric). Throughout the paper we denote as well other conditions of pseudosymmetry type we refer the reader the papers: [1], [13]- [22], [44] and also references therein. We note that [20] is the first paper, in which manifolds…”

Section: Preliminariesmentioning

confidence: 99%

“…We mention that non-Roter type manifolds with the curvature tensor having a decomposition of the form (5.2) were already investigated in [44] and very recently in [19], [22]. Namely, [44] contains results on hypersurfaces in space forms having curvature tensors of the form (5.2). As it was shown in Section 2 of [19], the 4-dimensional manifold presented in Section 4 of [12] has the curvature tensor of the form (5.2).…”

Section: Some Examples Of Deszcz and Chaki Pseudosymmetric Manifoldsmentioning

confidence: 99%

On pseudosymmetric manifolds

Shaikh¹,

Deszcz²,

Hotlos³

et al. 2015

Publ. Math. Debrecen

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In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric [8]) manifold to be Deszcz pseudosymmetric (resp. Ricci pseudosymmetric). We also study the necessary and sufficient conditions for a weakly symmetric [58] (resp. weakly Ricci symmetric [59]) manifold by Tam\'assy and Binh to be Deszcz pseudosymmetric (resp. Ricci pseudosymmetric). We also obtain the reduced form of the defining condition of weakly Ricci symmetric manifolds by Tam\'assy and Binh [59]. Finally we give some examples to show the independent existence of such types of pseudosymmetry which also ensure the existence of Roter type and generalized Roter type manifolds and the manifolds with recurrent curvature 2-form ([2], [29]) associated to various curvature tensors.Comment: 32 page

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“…If p n − p − 1 then in view of Theorem 3.2 the Riemann-Christoffel curvature tensor R of the cone M is expressed at every point by a linear combination of the tensors ∧ , ∧ S and S ∧ S, ∧ S 2 , S ∧ S 2 and S 2 ∧ S 2 . We refer to [50] and [52] for further results on hypersurfaces with the curvature tensor having the above presented property. Now (39), by (3.9) of [23], and the conditions κ = 0 and ψ = − εκ n−1 , reduces on U H to…”

Section: Hypersurfaces In Spaces Of Constant Curvaturementioning

confidence: 99%