title: Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics)
author:  Wulf Rossmann 
description: <br>"[A]n excellent and original introductory course on Lie groups."--<em>Zentralblatt MATH</em>
zlib_text: ![](Images/image00161.jpeg)
  
  ISOMETRIC ACTIONS OF LIE GROUPS AND INVARIANTS
  
  Peter
  
  W.
  
  Michor
  
  Erwin Schrodinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090
  Wien, Austria
  
  and
  
  Institut fur Mathematik,
  
  Universitat Wien,
  
  Strudlhofgasse 4, A-1090 Wien, Austria.
  
  July 31, 1997
  
  This are the notes of a lecture course held by P. Michor at the University of
  Vienna in the academic year 1992/1993, written by Konstanze Rietsch. The
  lecture course was held again in the academic year 1996/97 and the notes were
  corrected and enlarged by P. Michor.
  
  T
  
  able
  
  of
  
  con
  
  ten
  
  ts
  
  1\. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
  
  2\. Polynomial Invariant Theory . . . . . . . . . . . . . . . . . . . . 5
  
  3\. C -Invariant Theory of Compact Lie Groups . . . . . . . . . . . . .
  
  1
  
  11
  
  4\. Transformation Groups . . . . . . . . . . . . . . . . . . . . . . . 34
  
  5\. Proper Actions . . . . . . . . . . . . . . . . . . . . . . . . . . 41
  
  6\. Riemannian G-manifolds . .