Conformal Killing vectors in nonexpanding -spaces with Λ

Chudecki, Adam

doi:10.1088/0264-9381/27/20/205004

Cited by 8 publications

(55 citation statements)

References 28 publications

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“…It appeared, that HH-spaces are the most natural tool in investigating real spaces of the neutral (ultrahyperbolic) signature (+ + −−). Moreover, a few works devoted to Killing symmetries in heavenly and hyperheavenly spaces appeared [27][28][29][30]. These papers generalized the previous ideas of Plebański, Finley III and Sonnleitner [16][17][18].…”

Section: Introductionmentioning

confidence: 80%

Null Killing vectors and geometry of null strings in Einstein spaces

Chudecki

2014

Gen Relativ Gravit

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Einstein complex spacetimes admitting null Killing or null homothetic Killing vectors are studied. Such vectors define totally null and geodesic 2-surfaces called the null strings or twistor surfaces. Geometric properties of these null strings are discussed. It is shown, that spaces considered are hyperheavenly spaces (HH-spaces) or, if one of the parts of the Weyl tensor vanishes, heavenly spaces (H-spaces). The explicit complex metrics admitting null Killing vectors are found. Some Lorentzian and ultrahyperbolic slices of these metrics are discussed.

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Section: Introductionmentioning

confidence: 80%

Null Killing vectors and geometry of null strings in Einstein spaces

Chudecki

2014

Gen Relativ Gravit

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“…The real Lorentzian case has been analyzed in details elsewhere (see [25] and references therein). We only mention here, that the space of the type {[N] n ⊗ [N] n , [−−]} is the only non-conformally or non-half-conformally flat space which admits a proper conformal vector (see [3] for complex case). The last remaining field equation (3.23d) reduces to the equation…”

Section: Field Equationsmentioning

confidence: 99%

Classification of complex and real vacuum spaces of the type [N] ⊗ [N]

Chudecki

2018

Journal of Mathematical Physics

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Complex and real, vacuum spaces with both self-dual and anti-self-dual parts of the Weyl tensor being of the type [N] are considered. Such spaces are classified according to two criteria. The first one takes into account the properties of the congruences of totally null, geodesic 2-dimensional surfaces (the null strings). The second criterion is based on investigations of the properties of the intersection of these congruences. It is proved that there exist six distinct types of the [N] ⊗ [N] spaces. New examples of the Lorentzian slices of the complex metrics are presented. Also, some type [N] ⊗ [N] spaces which do not posses Lorentzian slices are considered.

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“…One of the problems which, from the very beginning, has attracted a great deal of interest was the problem of classifying all H and HH-spaces admitting (conformal, homothetic or isometric) Killing vector [7] - [9], [13] - [16]. It seems that the only case which has been not analysed in that context is the case of complex H-space with Λ.…”

Section: Introductionmentioning

confidence: 99%