scholarly journals Equivariant quantizations and Cartan connections

2007 ◽  
Vol 13 (5) ◽  
pp. 857-874
Author(s):  
P. Mathonet
Keyword(s):  
2000 ◽  
Vol 29 (3) ◽  
pp. 453-505 ◽  
Author(s):  
Andreas ČAP ◽  
Hermann SCHICHL

2011 ◽  
Vol 08 (01) ◽  
pp. 177-185 ◽  
Author(s):  
MARCO FERRARIS ◽  
MAURO FRANCAVIGLIA ◽  
MARCELLA PALESE ◽  
EKKEHART WINTERROTH

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.


Author(s):  
E. Falbel ◽  
M. Mion-Mouton ◽  
J. M. Veloso

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.


2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Ivan Beschastnyi ◽  
Karen Habermann ◽  
Alexandr Medvedev

Author(s):  
Yu. I. Shevchenko

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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