DOUBROV, Boris and Jan SLOVÁK. Inclusions between parabolic geometries. Pure and Applied Mathematics Quarterly. Boston: Int. Press, 2010, vol. 6, No 3, p. 755-780. ISSN 1558-8599.
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Basic information
Original name Inclusions between parabolic geometries
Name in Czech Vkládání parabolických geometrií
Authors DOUBROV, Boris (112 Belarus) and Jan SLOVÁK (203 Czech Republic, guarantor, belonging to the institution).
Edition Pure and Applied Mathematics Quarterly, Boston, Int. Press, 2010, 1558-8599.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
Impact factor Impact factor: 0.462
RIV identification code RIV/00216224:14310/10:00045268
Organization unit Faculty of Science
UT WoS 000274658900007
Keywords (in Czech) Cartanovy konexe, Feffermanova konstrukce, volne distribuce, spinorova geometrie, normalita
Keywords in English Cartan connections; Fefferman construction; free distributions; spinorial geometry; normality conditions
Tags Cartan connections, fefferman constructions, parabolic geometries, weyl connections
Tags International impact, Reviewed
Changed by Changed by: prof. RNDr. Jan Slovák, DrSc., učo 1424. Changed: 21. 9. 2011 06:20.
Abstract
Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of the classical Onishchik's lists [10] and we treat the only new series of inclusions in detail, providing the spinorial structures on the manifolds with generic free distributions. Our technique relies on the cohomological understanding of the canonical normal Cartan connections for parabolic geometries and the classical computations with exterior forms. Apart of the complete discussion of the distributions from the geometrical point of view and the new functorial construction of the inclusion into the spinorial geometry, we also discuss the normality problem of the resulting spinorial connections. In particular, there is a non-trivial subclass of distributions providing normal spinorial connections directly by the construction.
Abstract (in Czech)
Některé z Feffermanovych konstrukcí parabolických geometrií vedou ke strukturám na téže varietě. V článku klasifikujeme vsechny tyto případy s pomocí klasických výsledků Oniščika, což vede také na spinorové geometrie pro volné distribuce.Technicky se opíráme o pochopení kohomologické podstaty Cartanových konexí v parabolických geometriích a klasický kalkul s vnějšími formami. Vedle geometrické diskuse vlastnosti funktroiálních konstrukcí zkoumáme také problém normality výsledné konexe. Zejména ukazujeme existenci netriviální třídy distribucí, pro které konstrukce dává přímo normální konexi.
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GA201/08/0397, research and development projectName: Algebraické metody v geometrii a topologii
Investor: Czech Science Foundation, Standard Projects
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