Recent research in Affine Differential Geometry
نویسنده
چکیده
In this paper we emphasize the geometry of affine immersions, widely developed in recent years. Mathematics Subject Classification: 01-02, 01A65.
منابع مشابه
RESEARCH STATEMENT ( revised 10 / 01 / 08 )
My work focuses on the geometry and differential equations invariant under groups of affine and projective motions (in R and RP respectively). In particular, affine differential geometry, the study of properties of hypersurfaces in R which are invariant under affine volume-preserving motions, informs most of my work. Affine differential geometry is an old subfield of geometry, with Blaschke mak...
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In the following we will give an overview of our research area. Most of it belongs to the field of affine differential geometry. Geometry, as defined in Felix Klein’s Erlanger Programm, is the theory of invariants with respect to a given transformation group. In this sense affine geometry corresponds to the affine group (general linear transformations and translations) and it’s subgroups acting...
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Affine spheres were introduced by Ţiţeica in [72, 73], and studied later by Blaschke, Calabi, and Cheng-Yau, among others. These are hypersurfaces in affine R which are related to real Monge-Ampère equations, to projective structures on manifolds, and to the geometry of Calabi-Yau manifolds. In this survey article, we will outline the theory of affine spheres their relationships to these topics...
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تاریخ انتشار 2005