Weyl structures for parabolic geometries

SLOVÁK, Jan and Andreas CAP. Weyl structures for parabolic geometries. Mathematica Scandinavica. Aarhus: Aarhus Universitet, vol. 93, No 1, p. 53-90. ISSN 0025-5521. 2003.

Basic information

• Original name: Weyl structures for parabolic geometries
• Authors: SLOVÁK, Jan (203 Czech Republic, guarantor) and Andreas CAP (40 Austria).
• Edition: Mathematica Scandinavica, Aarhus, Aarhus Universitet, 2003, 0025-5521.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Denmark
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 0.328
• RIV identification code: RIV/00216224:14310/03:00008190
• Organization unit: Faculty of Science
• UT WoS: 000186229900004
• Keywords in English: Cartan Connection; Parabolic Geometry; Weyl Structure; Conformal Geometry
• Tags: Cartan connection, Conformal Geometry, parabolic geometry, Weyl Structure

Abstract

Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures and preferred connections are introduced in this general framework. In particular, we extend the notions of scales, closed and exact Weyl connections, and Rho--tensors, we characterize the classes of such objects, and we use the results to give a new description of the Cartan bundles and connections for all parabolic geometries.

Links

• GA201/99/0296, research and development project: Name: Diferenciální geometrie vyššího řádu

Investor: Czech Science Foundation, Differential geometry of higher order

• MSM 143100009, plan (intention): Name: Matematické struktury algebry a geometrie

Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures of algebra and geometry