scholarly journals An Approach to the Cartan Geometry I: Conformal Riemann Manifolds

2019 ◽  
Author(s):  
Masatake Kuranishi
Keyword(s):  
Cartan Geometry ◽  
Riemann Manifolds

scholarly journals On Symmetric Cauchy–Riemann Manifolds

2000 ◽  
Vol 149 (2) ◽  
pp. 145-181 ◽  
Author(s):  
Wilhelm Kaup ◽  
Dmitri Zaitsev
Keyword(s):  
Riemann Manifolds ◽  
Cauchy Riemann

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.

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