Generalized Affine Symmetric Spaces

✍ Scribed by Oldřich Kowalski

• Publisher: John Wiley and Sons
• Year: 1977
• Tongue: English
• Weight: 245 KB
• Volume: 80
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19770800115

✦ Synopsis

In [Z] we have introduced and studied generalized symmetric RIEafA"ian spaces. In the present paper we introduce the concept of a generalized affine symmetric space. We also define the group of transvections of such a space, m d we give s ~m e basic properties of this group.

Following 0. LOOS, a symmetric space is a smooth manifold M (of the class C") together with a family (8,}zcH of diffeomorphisms satisfying the following axioms : ( t o ) z is an isolated fixed point Of sZ (20) (s,)x=iclentity (30) s, o sp = s, o s , , where z = sz( y )