On Riemann and Weyl compatible tensors

Deszcz, Ryszard; Głogowska, Małgorzata; Jełowicki, Jan; Petrović–Torgašev, Miroslava; Zafindratafa, Georges

doi:10.2298/pim1308111d

Cited by 38 publications

(30 citation statements)

References 32 publications

(27 reference statements)

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“…In particular, it was well-known that Robertson-Walker spacetimes are quasi-Einstein (see, e.g., [17]). …”

Section: A Pseudo Riemannian Manifold (M G) Is Called a Quasi-einstementioning

confidence: 99%

Classification of torqued vector fields and its applications to Ricci solitons

Chen¹

2017

Kragujevac J Math

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Abstract. Recently, the author defined torqued vector fields in [Kragujevac J. Math. 41(1) (2017), [93][94][95][96][97][98][99][100][101][102][103]. In this paper, we classify all torqued vector fields on Riemannian manifolds. Moreover, we investigate Ricci solitons with torqued potential fields. In particular, we prove that every Ricci soliton with torqued potential field is an almost quasi-Einstein manifold; and it is an Einstein manifold if and only if the potential field is a concircular vector field. Some related results on Ricci solitons are also obtained.

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“…In particular, it was well-known that Robertson-Walker spacetimes are quasi-Einstein (see, e.g., [17]). …”

Section: A Pseudo Riemannian Manifold (M G) Is Called a Quasi-einstementioning

confidence: 99%

Classification of torqued vector fields and its applications to Ricci solitons

Chen¹

2017

Kragujevac J Math

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“…A symmetric (0, 2)-tensor E on M is called Riemann compatible or R-compatible [59,60] (see also [30]) if on M we have R(EX 1 , X, X 2 , X 3 ) + R(EX 2 , X, X 3 , X 1 ) + R(EX 3 , X, X 1 , X 2 ) = 0, for all X, X 1 , X 2 , X 3 ∈ χ(M ), where E is the endomorphism on χ(M ) defined as…”

Section: Preliminariesmentioning

confidence: 99%

“…Again a vector field Y with associated 1-form Θ, i.e., g(Y, X) = Θ(X) is called Riemann compatible or R-compatible [30,60] if…”

Section: Preliminariesmentioning

confidence: 99%

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Curvature properties of some 4-dimensional semi-Riemannian metrics

A.¹,

Matsuyama²

2017

Kragujevac J Math

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“…Similarly we can define conformal compatibility (also known as Weyl compatibility see, [14] and [24]), concircular compatibility and conharmonic compatibility.…”

Section: Again a 1-form π Is Said To Be Riemann Compatible If π ⊗ π Imentioning

confidence: 99%

On curvature properties of Som–Raychaudhuri spacetime

Shaikh

Kundu

2016

J. Geom.

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Abstract. Som-Raychaudhuri [32] spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is shown that such a spacetime is a 2-quasiEinstein, generalized Roter type, Ein(3) manifold satisfying R.R = Q(S, R), C · C = 2a 2 3 Q(g, C), and its Ricci tensor is cyclic parallel and Riemann compatible. Finally, we make a comparison between Gödel spacetime and Som-Raychaudhuri spacetime.

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On Riemann and Weyl compatible tensors

Abstract: We investigate semi-Riemannian manifolds satisfying some curvature conditions. Those conditions are strongly related to pseudosymmetry.

Cited by 38 publications

References 32 publications

Classification of torqued vector fields and its applications to Ricci solitons

Classification of torqued vector fields and its applications to Ricci solitons

Curvature properties of some 4-dimensional semi-Riemannian metrics

On curvature properties of Som–Raychaudhuri spacetime

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