scholarly journals Cones and Cartan geometry

2021 ◽  
Vol 78 ◽  
pp. 101793
Author(s):  
Antonio J. Di Scala ◽  
Carlos E. Olmos ◽  
Francisco Vittone
Keyword(s):  
Cartan Geometry

CAN TORSION BE TREATED AS JUST ANOTHER TENSOR FIELD?

2012 ◽  
Vol 07 ◽  
pp. 158-164 ◽  
Author(s):  
JAMES M. NESTER ◽  
CHIH-HUNG WANG
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Affine Connection ◽  
Cartan Geometry ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Alternative Gravity Theories ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity ◽  
Alternative Gravity

Many alternative gravity theories use an independent connection which leads to torsion in addition to curvature. Some have argued that there is no physical need to use such connections, that one can always use the Levi-Civita connection and just treat torsion as another tensor field. We explore this issue here in the context of the Poincaré Gauge theory of gravity, which is usually formulated in terms of an affine connection for a Riemann-Cartan geometry (torsion and curvature). We compare the equations obtained by taking as the independent dynamical variables: (i) the orthonormal coframe and the connection and (ii) the orthonormal coframe and the torsion (contortion), and we also consider the coupling to a source. From this analysis we conclude that, at least for this class of theories, torsion should not be considered as just another tensor field.

scholarly journals The gap phenomenon in parabolic geometries

2017 ◽  
Vol 2017 (723) ◽  
Author(s):  
Boris Kruglikov ◽  
Dennis The
Keyword(s):  
Symmetry Algebra ◽  
Maximum Dimension ◽  
Cartan Geometry ◽  
Infinitesimal Symmetry ◽  
Parabolic Geometries

AbstractThe infinitesimal symmetry algebra of any Cartan geometry has maximum dimension realized by the flat model, but often this dimension drops significantly when considering non-flat geometries, so a gap phenomenon arises. For general (regular, normal) parabolic geometries of type

scholarly journals A new look at Newton–Cartan gravity

2016 ◽  
Vol 31 (24) ◽  
pp. 1630040 ◽  
Author(s):  
E. A. Bergshoeff ◽  
J. Rosseel
Keyword(s):  
Gravity Model ◽  
Cartan Geometry ◽  
Short Overview ◽  
New Look

We give a short overview of Newton–Cartan geometry and gravity including its matter couplings. We also present results on a new non-relativistic gravity model in three spacetime dimensions, called extended Bargmann gravity, and show that this model has matter couplings that differ from those of Newton–Cartan gravity.

scholarly journals Construction of Real Space{Time from Complex Linear Metric Connections

1997 ◽  
Vol 50 (4) ◽  
pp. 793
Author(s):  
P. K. Smrz
Keyword(s):  
Complex Manifold ◽  
Real Space ◽  
Space Time ◽  
Cartan Geometry ◽  
Four Dimensions ◽  
Linear Connections ◽  
Real Submanifold ◽  
Complex Linear ◽  
Case Based ◽  
Construction Works

A construction of real space-time based on metric linear connections in a complex manifold is described. The construction works only in two or four dimensions. The four-dimensional case based on a connection reducible to group U(2, 2) can generate Riemann-Cartan geometry on the real submanifold of the original complex manifold. The possibility of connecting the appearance of Dirac fields with anholonomic complex frames is discussed.

scholarly journals Branched holomorphic Cartan geometry on Sasakian manifolds

2020 ◽  
Vol 24 (2) ◽  
pp. 259-278
Author(s):  
Indranil Biswas ◽  
Sorin Dumitrescu ◽  
Georg Schumacher
Keyword(s):  
Sasakian Manifolds ◽  
Cartan Geometry

scholarly journals Lax pairs for string Newton Cartan geometry

2020 ◽  
Vol 954 ◽  
pp. 114990 ◽  
Author(s):  
Dibakar Roychowdhury
Keyword(s):  
Lax Pairs ◽  
Cartan Geometry
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