Dillen, Franki; Vrancken, Luc Affine differential geometry of hypersurfaces. (English) Zbl 0727.53017 Geometry and topology of submanifolds II, Proc. Int. Meet., Avignon/Fr. 1988, 144-164 (1990). [For the entire collection see Zbl 0727.00009.] The purpose of this survey is to give an idea of what affine differential geometry is about and of the kind of problems in which affine differential geometers are interested. This exposition will be elementary and can be considered as an introduction to affine differential geometry. We will restrict ourselves to the affine differential geometry of hypersurfaces of the real affine space. We will follow the approach as given by K. Nomizu [What is affine differential geometry? Differential Geometry Meeting, Univ. Münster 1982, Tagungsbericht 42-43 (1982)] at a conference in Münster in 1982. If we talk about hypersurfaces, we mean immersed hypersurfaces, but we will very often disregard the immersion. In other words, for an immersed hypersurface \(M^ n\), immersed by x, we will identify \(M^ n\) and \(x(M^ n)\) and \(TM^ n\) and \(x_*(TM^ n)\), if there is no confusion possible. Cited in 2 Documents MSC: 53A15 Affine differential geometry 53-02 Research exposition (monographs, survey articles) pertaining to differential geometry Keywords:introduction to affine differential geometry; hypersurfaces Citations:Zbl 0727.00009 PDFBibTeX XML