International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 47, Pages 3007-3014
Chern-Simons forms of pseudo-Riemannian homogeneity on the
1Department of Mathematics, Institute of Mathematics and Fundamental Physics, Spanish Council for Scientific Research (CSIC), Serrano 144, Madrid 28006, Spain
2Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain
Received 17 October 2002
Copyright © 2003 P. M. Gadea and J. A. Oubiña. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider forms of Chern-Simons type associated to homogeneous
pseudo-Riemannian structures. The corresponding secondary classes
are a measure of the lack of a homogeneous pseudo-Riemannian
space to be locally symmetric. In the present paper, we compute
these forms for the oscillator group and the corresponding
secondary classes of the compact quotients of this group.