On classification of normal operators in real spaces with indefinite   scalar product
  A real finite-dimensional space with indefinite scalar product having v- negative squares and v+ positive ones is considered. The paper presents a classification of operators that are normal with respect to this product for the cases min{v-, v+} = 1, 2. The approach used here was developed in papers by Gohberg and Reichstein and by the authors, where a similar classification was obtained for complex spaces with v = min{v-,v+} = 1, 2, respectively. 
Olga Holtz, Vladimir Strauss