Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a path-independent geometrical functional using a global constraint on continuous functions. This paper generalizes this first step to Lorentzian geometry. We show that, in a...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146501 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry / N. Franco // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709494169993216 |
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| author | Franco, N. |
| author_facet | Franco, N. |
| citation_txt | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry / N. Franco // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a path-independent geometrical functional using a global constraint on continuous functions. This paper generalizes this first step to Lorentzian geometry. We show that, in a globally hyperbolic spacetime, a single global timelike eikonal condition is sufficient to construct a path-independent Lorentzian distance function.
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| first_indexed | 2025-12-07T17:17:38Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146501 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:17:38Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Franco, N. 2019-02-09T19:27:42Z 2019-02-09T19:27:42Z 2010 Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry / N. Franco // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58B34; 53C50 DOI:10.3842/SIGMA.2010.064 https://nasplib.isofts.kiev.ua/handle/123456789/146501 Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a path-independent geometrical functional using a global constraint on continuous functions. This paper generalizes this first step to Lorentzian geometry. We show that, in a globally hyperbolic spacetime, a single global timelike eikonal condition is sufficient to construct a path-independent Lorentzian distance function. This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
 We would like to thank the anonymous referees for their useful remarks and relevant contribution to this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry Article published earlier |
| spellingShingle | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry Franco, N. |
| title | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_full | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_fullStr | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_full_unstemmed | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_short | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_sort | global eikonal condition for lorentzian distance function in noncommutative geometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146501 |
| work_keys_str_mv | AT francon globaleikonalconditionforlorentziandistancefunctioninnoncommutativegeometry |