Open AccessAffine 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.