International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 47, Pages 3007-3014

Chern-Simons forms of pseudo-Riemannian homogeneity on the oscillator group

P. M. Gadea1 and J. A. Oubiña2

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.