Weyl Invariant Spacetime

Abstract

A new class of Weyl invariant backgrounds are presented in terms of the metric $G_{\mu \nu }$ and the anti-symmetric Kalb-Ramond fields $B_{\mu \nu }$. The ten-dimensional spacetime is a product of four-dimensional flat spacetime and curved six-dimensional spacetime having nonvanishing Ricci tensors. The non-vanishing Kalb-Ramond field strengths cannot be written globally as $H=dB$, being of the monopole type. Nevertheless they define homogeneous spacetime with no singularity.

12 pages