Lie groups occupy a central position in modern differential geometry and physics, as they are very useful for describing the continuous symmetries of a space. This paper is an expository article meant to introduce the theory of Lie groups, as well as survey some results related to the Riemannian geometry of groups admitting invariant metrics. In particular, a non-standard proof of the classification of invariant metrics is presented. For those unfamiliar with tensor calculus, a section devoted to tensors on manifolds and the Lie derivative is included.
Dr. Po Lam Yung, Assistant Professor of Mathematics, The Chinese University of Hong Kong.
Geis, Michael L.
"Notes on the Riemannian Geometry of Lie Groups,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 5.
Available at: http://scholar.rose-hulman.edu/rhumj/vol15/iss2/5