caa a22 4500 467989125 CHVBK 20180323112540.0 cr unu---uuuuu 170328e19900901xx s 000 0 eng 10.1007/BF01297762 doi (NATIONALLICENCE)springer-10.1007/BF01297762 Conjugate connections and Radon's theorem in affine differential geometry [Elektronische Daten] [Franki Dillen, Katsumi Nomizu, Luc Vranken] For a given nondegenerate hypersurfaceM n in affine space ℝ n+1 there exist an affine connection ∇, called the induced connection, and a nondegenerate metrich, called the affine metric, which are uniquely determined. The cubic formC=∇h is totally symmetric and satisfies the so-called apolarity condition relative toh. A natural question is, conversely, given an affine connection ∇ and a nondegenerate metrich on a differentiable manifoldM n such that ∇h is totally symmetric and satisfies the apolarity condition relative toh, canM n be locally immersed in ℝ n+1 in such a way that (∇,h) is realized as the induced structure? In 1918J. Radon gave a necessary and sufficient condition (somewhat complicated) for the problem in the casen=2. The purpose of the present paper is to give a necessary and sufficient condition for the problem in casesn=2 andn≥3 in terms of the curvature tensorR of the connection ∇. We also provide another formulation valid for all dimensionsn: A necessary and sufficient condition for the realizability of (∇,h) is that the conjugate connection of ∇ relative toh is projectively flat. Springer-Verlag, 1990 Dillen Franki Department Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3030, Leuven, Belgium aut Nomizu Katsumi Mathematical Department, Brown University, 02912, Providence, RI, USA aut Vranken Luc Department Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3030, Leuven, Belgium aut Monatshefte für Mathematik Springer-Verlag 109/3(1990-09-01), 221-235 0026-9255 109:3<221 1990 109 605 https://doi.org/10.1007/BF01297762 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01297762 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dillen Franki Department Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3030, Leuven, Belgium aut NATIONALLICENCE 700 1- Nomizu Katsumi Mathematical Department, Brown University, 02912, Providence, RI, USA aut NATIONALLICENCE 700 1- Vranken Luc Department Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3030, Leuven, Belgium aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer-Verlag 109/3(1990-09-01), 221-235 0026-9255 109:3<221 1990 109 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer