The pedal of hypersurface with a constant support function (original) (raw)

Abstract

The locus of the foot of the perpendicular from a point O to a tangent hyperplane of a given hypersurface M in Euclidean space E n+1 is called the pedal of M with respect to O. Applications of the pedal in differential geometry can be found in papers by Th. Hasanis and D. Koutroufiotis [J. Geom. 24, 131-167 (1985; Zbl 0578.53002)], Chr. Georgiou, Th. Hasanis and D. Koutroufiotis [Geom. Dedicata 28, 153-169 (1988; Zbl 0659.53004)]. In the paper under review, the authors try to study the differential geometry of the pedal of a hypersurface with a constant support function. The study is trivial since in that case the pedal is a hypersphere. Euclidean hypersurfaces with a constant support function have been classified by Th. Hasanis and D. Koutroufiotis [Arch. Math. 57, 189-192 (1991; Zbl 0697.53012)].

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