Accession Number : AD0818854

Title :   A GEOMETRIC CONFIGURATION ASSOCIATED WITH THE OSCULATING QUADRICS AT A POINT OF AN ANALYTIC SURFACE.

Descriptive Note : Informal rept.,

Corporate Author : NAVAL OCEANOGRAPHIC OFFICE NSTL STATION MS HYDROGRAPHIC DEVELOPMENT DIV

Personal Author(s) : Thomas, Paul D.

Report Date : MAY 1967

Pagination or Media Count : 34

Abstract : By considering certain polar reciprocal relations between the osculating quadrics of Darboux and of Bompiani at a given point of an analytic surface, the resulting geometric configuration was studied. Plane loci discovered included conics, cubics, quartics, and sextics. Space loci discovered included twisted cubics, quadric cones, osculating planes, ruled cubic surface, tangent developable quartic surfaces, osculating linear complexes and null systems of twisted cubics, a skew involution, and a linear congruence. (Author)

Descriptors :   (*GEOMETRIC FORMS, VECTOR SPACES), DIFFERENTIAL GEOMETRY, MATRICES(MATHEMATICS), LOCUS, ANALYTIC GEOMETRY, PROJECTIVE GEOMETRY, INEQUALITIES, DIFFERENTIAL EQUATIONS, EQUATIONS, POLYNOMIALS.

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE