Note on (conformally) semi-symmetric spacetimes

Eriksson, Ingemar; Senovilla, José M. M.

doi:10.1088/0264-9381/27/2/027001

Cited by 19 publications

(14 citation statements)

References 14 publications

(23 reference statements)

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“…To prove this, we use the Petrov classification [12]. By [7] we know that all the semi-symmetric spacetimes (of dimension 4) are of type D, N or O. Moreover, as a consequence of this result, it was also proven that the 2-symmetric spacetimes are of Petrov type N , or its degenerate case, O.…”

Section: Sketch Of the Proof Of Theorem 11mentioning

confidence: 94%

Spanish Relativity Meeting/ERE2009 Gravitation in the Large

Lazkoz¹,

Vera²

2010

J. Phys.: Conf. Ser.

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Abstract. We present the explicit local form of the metric of the second-order symmetric non-symmetric 4-dimensional Lorentzian manifolds. They turn out to be a specific subclass of plane waves. IntroductionThe historical roots of the subject under investigation go back to the classification of the locally symmetric spaces in the (proper) Riemannian case by Cartan [2,3]. Locally symmetric pseudoRiemannian manifolds are characterized by the condition ∇R = 0, where R denotes the curvature tensor of the manifold. The pseudo-Riemannian manifolds satisfying ∇ 2 R = 0 constitute a logical generalization of the locally symmetric ones. But in the Riemannian case these two conditions are equivalent. Moreover, in the Riemannian case:

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Section: Sketch Of the Proof Of Theorem 11mentioning

confidence: 94%

Spanish Relativity Meeting/ERE2009 Gravitation in the Large

Lazkoz¹,

Vera²

2010

J. Phys.: Conf. Ser.

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“…Using the spinor formalism with the standard notation [12,13] for the curvature spinors, the semi-symmetric conditions ∇ [a ∇ b] R cdef = 0 can be rewritten as: (1) and (2)] =⇒ (3) (C = 0) [8]. Similarly [ (1) and (3)] =⇒ (2) [6].…”

Section: The Spinor Inspirationmentioning

confidence: 99%

“…(i) n ≥ 5 for all signatures [3,9] (ii) n = 4 for Lorentz signature (using spinors) [8] that semi-symmetry [2,14,15] is equivalent to conformal semi-symmetry when the Weyl conformal tensor C abcd is non-zero:…”

Section: Introductionmentioning

confidence: 99%

(Conformally) semisymmetric spaces and special semisymmetric Weyl tensors

Edgar¹,

Senovilla²

2011

J. Phys.: Conf. Ser.

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“…Extensions to other signatures and to non-simply-connected cases are also available, see Cahen and Parker [9], Neukirchner [33] and specially Kath and Olbrich [26,27]. Lorentzian semi-symmetric spaces have also been studied in the literature, see for instance their classification in four dimensions [16,22] and references therein. Nevertheless, prior to the paper [37] by one of the authors, the 2nd-symmetric spaces had not been studied systematically.…”

Section: Introductionmentioning

confidence: 99%

Structure of second-order symmetric Lorentzian manifolds

Blanco¹,

Sánchez²,

Senovilla³

2013

J. Eur. Math. Soc.

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Abstract. Second-order symmetric Lorentzian spaces, that is to say, Lorentzian manifolds with vanishing second derivative ∇∇R ≡ 0 of the curvature tensor R, are characterized by several geometric properties, and explicitly presented. Locally, they are a product M = M 1 × M 2 where each factor is uniquely determined as follows: M 2 is a Riemannian symmetric space and M 1 is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen-Wallach family. In the proper case (i.e., ∇R = 0 at some point), the curvature tensor turns out to be described by some local affine function which characterizes a globally defined parallel lightlike direction. As a consequence, the corresponding global classification is obtained, namely: any complete second-order symmetric space admits as universal covering such a product M 1 × M 2 . From the technical point of view, a direct analysis of the second-symmetry partial differential equations is carried out leading to several results of independent interest relative to spaces with a parallel lightlike vector field -the so-called Brinkmann spaces.

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Note on (conformally) semi-symmetric spacetimes

Abstract: Abstract. We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.

Cited by 19 publications

References 14 publications

Spanish Relativity Meeting/ERE2009 Gravitation in the Large

Spanish Relativity Meeting/ERE2009 Gravitation in the Large

(Conformally) semisymmetric spaces and special semisymmetric Weyl tensors

Structure of second-order symmetric Lorentzian manifolds

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