scholarly journals Equivariant quantizations and Cartan connections

2007 ◽  
Vol 13 (5) ◽  
pp. 857-874
Author(s):  
P. Mathonet
Keyword(s):  
Cartan Connections

scholarly journals Parabolic geometries and canonical Cartan connections

2000 ◽  
Vol 29 (3) ◽  
pp. 453-505 ◽  
Author(s):  
Andreas ČAP ◽  
Hermann SCHICHL
Keyword(s):  
Cartan Connections ◽  
Parabolic Geometries

GAUGE-NATURAL NOETHER CURRENTS AND CONNECTION FIELDS

2011 ◽  
Vol 08 (01) ◽  
pp. 177-185 ◽  
Author(s):  
MARCO FERRARIS ◽  
MAURO FRANCAVIGLIA ◽  
MARCELLA PALESE ◽  
EKKEHART WINTERROTH
Keyword(s):  
Variational Problems ◽  
Conserved Quantities ◽  
Cartan Connections ◽  
Natural Bundles

We study geometric aspects concerned with symmetries and conserved quantities in gauge-natural invariant variational problems and investigate implications of the existence of a reductive split structure associated with canonical Lagrangian conserved quantities on gauge-natural bundles. In particular, we characterize the existence of covariant conserved quantities in terms of principal Cartan connections on gauge-natural prolongations.

scholarly journals Cartan connections and path structures with large automorphism groups

2021 ◽  
Author(s):  
E. Falbel ◽  
M. Mion-Mouton ◽  
J. M. Veloso
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Compact Manifolds ◽  
Contact Form ◽  
Cartan Connection ◽  
Cartan Connections ◽  
Path Structure

In this paper, we classify compact manifolds of dimension three equipped with a path structure and a fixed contact form (which we refer to as a strict path structure) under the hypothesis that their automorphism group is non-compact. We use a Cartan connection associated to the structure and show that its curvature is constant.

scholarly journals Cartan Connections for Stochastic Developments on sub-Riemannian Manifolds

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Ivan Beschastnyi ◽  
Karen Habermann ◽  
Alexandr Medvedev
Keyword(s):  
Riemannian Manifolds ◽  
Cartan Connections

Curvature-torsion quasitensor of Laptev fundamental-group connection

2020 ◽  
pp. 155-169
Author(s):  
Yu. I. Shevchenko
Keyword(s):  
Fundamental Group ◽  
Curvature Tensor ◽  
Principal Bundle ◽  
Torsion Tensor ◽  
Structural Equations ◽  
The Other ◽  
Cartan Connection ◽  
Cartan Connections ◽  
Special Cases ◽  
The Given

We consider a space with Laptev's fundamental group connection generalizing spaces with Cartan connections. Laptev structural equations are reduced to a simpler form. The continuation of the given structural equations made it possible to find differential comparisons for the coeffi­cients in these equations. It is proved that one part of these coefficients forms a tensor, and the other part forms is quasitensor, which justifies the name quasitensor of torsion-curvature for the entire set. From differential congruences for the components of this quasitensor, congruences are ob­tained for the components of the Laptev curvature-torsion tensor, which contains 9 subtensors included in the unreduced structural equations. In two special cases, a space with a fundamental connection is a spa­ce with a Cartan connection, having a quasitensor of torsion-curvature, which contains a quasitensor of torsion. In the reductive case, the space of the Cartan connection is turned into such a principal bundle with connec­tion that has not only a curvature tensor, but also a torsion tensor.

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