Affine differential geometry of osculating hypersurfaces | Zendy

Kazimieras Navickis | Zendy

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Affine differential geometry of osculating hypersurfaces

Author(s) -

Kazimieras Navickis

Publication year - 2012

Publication title -

lietuvos matematikos rinkinys

Language(s) - English

Resource type - Journals

eISSN - 2335-898X

pISSN - 0132-2818

DOI - 10.15388/lmr.b.2012.07

Subject(s) - osculating circle , hypersurface , mathematics , affine transformation , affine geometry of curves , differential geometry , euclidean geometry , geometry , euclidean space , affine space , differential (mechanical device) , invariant (physics) , mathematical analysis , pure mathematics , physics , mathematical physics , thermodynamics

Osculating surfaces of second order have been studied in classical affine differential geometry [1]. In this article we generalize this notion to osculating hypersurfaces of higher order of hypersurfaces in Euclidean n-space. Various geometric interpretations are given. This yields a affinely invariant consideration of the local properties of a given hypersurface which depend on the derivatives of higher order.

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