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Journal of Mathematics
Volume 2016, Article ID 3681529, 10 pages
Research Article

Sectional and Ricci Curvature for Three-Dimensional Lie Groups

1Department of Mathematics, The University of Toledo, Toledo, OH 43606, USA
2Bristol Community College, Fall River, MA 02720, USA

Received 12 July 2016; Accepted 31 October 2016

Academic Editor: K. F. C. Yiu

Copyright © 2016 Gerard Thompson and Giriraj Bhattarai. 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.


Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.