Conformal Invariance in Einstein-Cartan-Weyl space
  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. In this case, we express conformally invariant action in terms of two
scalar fields of conformal weight -1, which can be cast into some interesting
form. We discuss some applications of the result.
