Canonical Centroaffine Hypersurfaces in Rn+1
Canonical Centroaffine Hypersurfaces in Rn+1
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DOI：
10.1007/bf03323203
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发表时间：
1991-11
影响因子：
2.2
通讯作者：
An-Min Li;Changping Wang
中科院分区：
文献类型：
--
作者：
An-Min Li;Changping Wang
Let x: M-4lR n+ l be a regular centroaffine hypersurface.· Then x induces a Pseudo· Riemannian meuic G on M called centroaffine metric and a cubic fonn C caJled Fubini-Pick fonn. As well known,(G, C) are centroaffine invariants which detennine x up to centroaffine transformations.Our purpose in this paper is to study a special class of centroaffine hypersurfaces in lR n+ 1 called canonical hypersur/aces. A cenlroaffine hypersurface is said to be canonical if its Blaschke meuic is flat and its Fubini-Pick form is parallel with. respect to its Blaschke metric. We reduce the classification problem of canonical hypersurfaces to the algebraic classification problem of n mutually commutative linear operators in lR n.\which are self-adjoint with respect to an indefinite inner product. Then we can use algebraic method to give many interesting examples of canonical hypersurfaces as follows:
