caa a22 4500 477094473 CHVBK 20180405111523.0 cr unu---uuuuu 170330e19960501xx s 000 0 eng 10.1007/BF03322221 doi (NATIONALLICENCE)springer-10.1007/BF03322221 Hug Daniel Mathematisches Institut, Albert-Ludwigs-Universität, Albertstraße 23b, D-79104, Freiburg i. Br, Germany aut Curvature Relations and Affine Surface Area for a General Convex Body and its Polar [Elektronische Daten] [Daniel Hug] We investigate the relationship between generalized curvatures of an arbitrary convex body K and its polar body K* in d-dimensional Euclidean space. For example, the generalized Gauß-Kronecker curvature of K is compared with the product of the generalized principal radii of curvature of K*. This leads to a generalization of the classical statement saying that the product of the equiaffine support functions of K and K* is equal to 1, provided K is sufficiently smooth and has positive Gauß-Kronecker curvature. Another consequence concerns the equality of the extended p-affine surface area of K and the q-affine surface area of K*, if pq = d2. In the special case of a smooth convex body and for p = d this result is well known in centroaffine differential geometry. Birkhäuser Verlag, Basel, 1996 52A20 nationallicence 52A40 nationallicence 53A15 nationallicence Generalized Gauß-Kronecker curvature nationallicence generalized principal radii of curvature nationallicence polar body nationallicence affine surface area nationallicence equiaffine support function nationallicence Results in Mathematics Birkhäuser-Verlag 29/3-4(1996-05-01), 233-248 0378-6218 29:3-4<233 1996 29 25 https://doi.org/10.1007/BF03322221 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF03322221 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hug Daniel Mathematisches Institut, Albert-Ludwigs-Universität, Albertstraße 23b, D-79104, Freiburg i. Br, Germany aut NATIONALLICENCE 773 0- Results in Mathematics Birkhäuser-Verlag 29/3-4(1996-05-01), 233-248 0378-6218 29:3-4<233 1996 29 25 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer