THE BRUCE-ROBERTS NUMBER OF A FUNCTION ON A WEIGHTED HOMOGENEOUS HYPERSURFACE

2011 ◽  
Vol 64 (1) ◽  
pp. 269-280 ◽  
Author(s):  
J. J. Nuno-Ballesteros ◽  
B. Orefice ◽  
J. N. Tomazella
Keyword(s):  
Homogeneous Hypersurface

Characterization of isolated homogeneous hypersurface singularities in ℂ4

2006 ◽  
Vol 49 (11) ◽  
pp. 1576-1592 ◽  
Author(s):  
Kepao Lin ◽  
Zhenhan Tu ◽  
Stephen S. T. Yau
Keyword(s):  
Hypersurface Singularities ◽  
Homogeneous Hypersurface

scholarly journals A CHARACTERIZATION OF CAYLEY HYPERSURFACE AND EASTWOOD AND EZHOV CONJECTURE

2005 ◽  
Vol 16 (08) ◽  
pp. 841-862 ◽  
Author(s):  
YUNCHERL CHOI ◽  
HYUK KIM
Keyword(s):  
Affine Space ◽  
Inner Product ◽  
Symmetric Algebras ◽  
Homogeneous Hypersurface

Eastwood and Ezhov generalized the Cayley surface to the Cayley hypersurface in each dimension, proved some characteristic properties of the Cayley hypersurface and conjectured that a homogeneous hypersurface in affine space satisfying these properties must be the Cayley hypersurface. We will prove this conjecture when the domain bounded by a graph of a function defined on ℝn is also homogeneous giving a characterization of Cayley hypersurface. The idea of the proof is to look at the problem of affine homogeneous hypersurfaces as that of left symmetric algebras with a Hessian type inner product. This method gives a new insight and powerful algebraic tools for the study of homogeneous affine hypersurfaces.

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