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Teoreticheskaya i Matematicheskaya Fizika, 2017, Volume 191, Number 2, Pages 243–253
DOI: https://doi.org/10.4213/tmf9202
(Mi tmf9202)
 

Conformal reference frames for Lorentzian manifolds

I. V. Maresin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
References:
Abstract: We define a conformal reference frame, i.e., a special projection of the six-dimensional sky bundle of a Lorentzian manifold (or the five-dimensional twistor space) to a three-dimensional manifold. We construct an example, a conformal compactification, for Minkowski space. Based on the complex structure on the skies, we define the celestial transformation of Lorentzian vectors, a kind of spinor correspondence. We express a $1$-form generating the contact structure in the twistor space (when it is smooth) explicitly as a form taking line-bundle values. We prove a theorem on the projection of this $1$-form to the fiberwise normal bundle of a reference frame; its corollary is an equation for the flow of time.
Keywords: Lorentzian manifold, sky, null geodesic, twistor, contact geometry, line bundle, spinor, conformal symmetry, light cone, Penrose compactification.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00117А
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0014-2015-0037
This research is supported in part by the Russian Foundation for Basic Research (Grant No. 16-01-00117 A, "Complex Problems in Mathematical Physics") and the Russian Academy of Sciences (Program No. I.37$\Pi$, "Nonlinear Dynamics in the Mathematical and Physical Sciences, Project No. 0014-2015-0037, "Complex and algebro-geometric methods in problems of nonlinear dynamics").
Received: 05.04.2016
English version:
Theoretical and Mathematical Physics, 2017, Volume 191, Issue 2, Pages 682–691
DOI: https://doi.org/10.1134/S0040577917050099
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. V. Maresin, “Conformal reference frames for Lorentzian manifolds”, TMF, 191:2 (2017), 243–253; Theoret. and Math. Phys., 191:2 (2017), 682–691
Citation in format AMSBIB
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\paper Conformal reference frames for Lorentzian manifolds
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  • https://doi.org/10.4213/tmf9202
  • https://www.mathnet.ru/eng/tmf/v191/i2/p243
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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