Conformal Invariance in Einstein-Cartan-Weyl space

Understand

We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions($>2$) and investigate the relations among them.

• In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion.
• In Einstein-Cartan space a similar role is played by the vector part of the torsion tensor.
• We consider the case where the trace part of the torsion is the Kalb-Ramond type of field.