The fundamental theorems of curves and hypersurfaces in centro-affine geometry | Zendy

Robert B. Gardner | Zendy; George R. Wilkens | Zendy

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The fundamental theorems of curves and hypersurfaces in centro-affine geometry

Author(s) -

Robert B. Gardner,

George R. Wilkens

Publication year - 1997

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1105733254

Subject(s) - affine transformation , mathematics , rigidity (electromagnetism) , affine geometry of curves , geometry , mathematical analysis , pure mathematics , affine group , physics , quantum mechanics

The motivation of this paper is to nd formulations of the local rigidity theorems for centro-ane curves and hypersurfaces that are amenable to direct application to problems in control theory. Elie Cartan’s method of moving frames develops the solutions in a natural way. The case of centro-ane curves has previously appeared only for certain low dimensions. This is the rst time a theory for curves in arbitrary dimensions has appeared.

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